c V2w02182j XKSuotea0 tSdoMfxtJ wxaKreeW HLNLwCZ.X l 2AKlYlo grsi3gkh4tpsE Er5eYsveFrZvuesdL.9 3 7MOa8dr ej uwkivtXhw wI4nPfoicnai0tMeV uA5ltg6e6burjaG f2H.

v Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 1
Name___________________________________
Date________________
H z2k021k2i EKduBtlaV KStoqf8tRwdaCrLeO bLcLUCv.T F RAglol1 gr7ijgnh1tJ sT lr4eFsrekrjveeYdd.j
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log
13
169 = 2 2) log
17
289 = 2
Rewrite each equation in logarithmic form.
3)

5
2
= 25 4)

8
2
= 64
Evaluate each expression.
5) log
4

1
64
6) log
2
4
7) log
4
16 8) log
49
7
9) log
7
49 10) log
3
9
11) log
4
64 12) log
6
36
13) log
2

1
32
14) log
3
243
Expand each logarithm.
15) log
9
(

w

u

v
)
16) log

a
2

b
4
17) log
2

x
6

y
5
18) log
2

(

x

y
3 )
3
Condense each expression to a single logarithm.
19)

6log
6

a

2log
6

b
20)

log
7

w +

log
7

u
2
+

log
7

v
2
21)

5log
5

x +

25log
5

y 22)

2log
7

x +

6log
7

y
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
4
5 =

A
log
4
9 =

B
log
4
6 =

C
Find log
4

5
81
24) log
5
6 =

X
log
5
8 =

Y
log
5
9 =

Z
Find log
5

8
81
25) log
4
10 =

U
log
4
6 =

V
log
4
9 =

W
Find log
4

27
20
26) log
7
6 =

M
log
7
8 =

P
log
7
10 =

Q
Find log
7
4800
D r270t132Y EKhuRtda3 6SOosfPtcwHayrweC rLzLxC5.U J pAzlhlH BrvisgfhwtLsj xrhezsze8r9vBePdm.u H EMKa7dXed 6wLiUtphJ tI7nSfmivn3iXtXeb aAxlcgNeRb2r4ao I 2R.5 Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 1)
1)

13
2
= 169 2)

17
2
= 289
3) log
5
25 = 2 4) log
8
64 = 2
5) 3 6) 2 7) 2
8)

1
2
9) 2 10) 2 11) 3 12) 2
13) 5 14) 5
15)

log
9

w +

log
9

u
2
+

log
9

v
2
16)

2log

a

4log

b 17)

6log
2

x

5log
2

y 18)

3log
2

x

9log
2

y
19) log
6

a
6

b
2
20) log
7
(

w

vu)
21) log
5
(

y
25

x
5
)
22) log
7
(

y
6

x
2
)
23)

A 2

B
24)

Y 2

Z 25)

2

W

V

U 26)

P +

M + 2

Q
4 I 2H0h1y2L mKYuPt0aB pSfodfFtQwZaUrNeL HLlLtC2.T E fAqlhls XrdilgGh1tysg 2rYeHsleprgvZeVdK.O W qMI aYdqeA vwHiFtwhi qICnTf2iPnWirtOeR fAqlbgheYbmrUaV F23.w Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 2
Name___________________________________
Date________________
h K2T0W1V2r gKjuPtvaJ CSroLfBtgwqaZrQel aL3L8C2.p y KA0lKlx trI ifgwhNt0sb rrpeps8eor5vweHd8.z
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log
4

r = 12 2) log

y

x = 15
Rewrite each equation in logarithmic form.
3)

8

p
=

1
3
4)

x
13
=

y
Evaluate each expression.
5) log
6
216 6) log
5
5
7) log
4

1
16
8) log
7
343
9) log
16

1
4
10) log
6
36
11) log
25
5 12) log
3
9
13) log
3
1 14) log
2
4
Expand each logarithm.
15) log
8
(

a

b

c
2
)
16) log
8
(

w
4

u
)
17) log
9

(

x
5

y
)
3
18) log
7

(

x
5

y
)
5
Condense each expression to a single logarithm.
19)

10log
5

x +

2log
5

y
20)

4log
6

w +

log
6

u
2
21)

log
4

x + log
4

y +

4log
4

z 22)

log
6

x + log
6

y +

2log
6

z
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
7
9 =

A
log
7
6 =

B
log
7
8 =

C
Find log
7

32
3
24) log
7
4 =

P
log
7
6 =

Q
log
7
9 =

R
Find log
7

27
2
25) log
8
10 =

R
log
8
7 =

S
log
8
12 =

T
Find log
8

1
1008
26) log
3
10 =

U
log
3
7 =

V
log
3
4 =

W
Find log
3
7000
O P2r0p1N2r 7KEuvtJ an gSvoqfbt9wya6rGep yLcLwCk.t 8 qA2lelb 1rziuggh4tSs3 erueOsAeqr7vAe2dE.7 F mMZaTdteF 4whittMh6 OIVnjfOibnwi8theo SAPlwgI eGbOrTa8 f25.F Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 2)
1)

4
12
=

r 2)

y
15
=

x
3) log
8

1
3
=

p
4) log

x

y = 13
5) 3 6) 1 7) 2 8) 3
9)

1
2
10) 2
11)

1
2
12) 2
13) 0 14) 2 15)

log
8

a + log
8

b +

2log
8

c
16)

4log
8

w +

log
8

u
2
17)

15log
9

x

3log
9

y 18)

25log
7

x

5log
7

y
19) log
5
(

y
2

x
10
)
20) log
6
(

w
4

u
)
21) log
4
(

yx

z
4
)
22) log
6
(

yx

z
2
)
23)

2

C

B 24)

Q +

R

P 25)

S 2

T 26)

V + 3

U
m l2W0I 1W2c yKmuztPa0 CSjoTfKtrwFasrge2 nLwLXCE.F C 7AAlilR 8rKisgehRtNsI urReWsueWrev3ezdZ.Q n GMgaPdne9 6wjiptahl 0IwnyfyianGiotLel eATlOgwebbXroaA 72h.D Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 3
Name___________________________________
Date________________
S I 2Q0Q1k2x LKmuotban tS6oYfntwwKaPryeo 2LDLcCY.g n GAalels 8rWi9gDhPtls2 irqePsde8r2vpendy.6
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log

5
8

b =

a
2) log

x

y =

1
2
Rewrite each equation in logarithmic form.
3)

a
12
= 98 4)

m

n
= 42
Evaluate each expression.
5) log
3
27 6) log
2
2
7) log
3
1
8) log
6

1
6
9) log
343

1
7
10) log
4

1
64
11) log
2
16 12) log
4
16
13) log
4
2 14) log
6
36
Expand each logarithm.
15) log
5
(

c

a

b)
16) log
7

x
3

y
3
17) log
7
(

c
3

a

b)
18) log
6

(

x

y
5
)
5
Condense each expression to a single logarithm.
19)

3log
4

x +

15log
4

y 20)

5log
2

u

5log
2

v
21)

log
3

x
2
+

log
3

y
2
+

log
3

z
2
22)

6ln

x

3ln

y
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
9
12 =

X
log
9
11 =

Y
log
9
8 =

Z
Find log
9
18
24) log
9
8 =

X
log
9
11 =

Y
log
9
6 =

Z
Find log
9
396
25) log
9
6 =

A
log
9
11 =

B
log
9
4 =

C
Find log
9

11
216
26) log6 =

X
log11 =

Y
log9 =

Z
Find log

54
121
U C2P0n1r2k wKjuftla0 XS0o3fCt8wxarrVeR 8LqLnCE.A d xAslMl5 frriPg6h5tqsR PrMeCsXesrBvBeXd6.2 D xMZawdNem FwkiPtahi fIyntf7iUnQiUtSe8 jAZlfgaeobWrcaV D2N.E Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 3)
1)

(

5
8
)

a
=

b
2)

x

1
2
=

y
3) log

a
98 = 12 4) log

m
42 =

n
5) 3 6) 1 7) 0 8) 1
9)

1
3
10) 3 11) 4 12) 2
13)

1
2
14) 2
15)

log
5

c +

log
5

a
2
+

log
5

b
2
16)

3log
7

x

3log
7

y
17)

log
7

c +

log
7

a
3
+

log
7

b
3
18)

5log
6

x +

25log
6

y
19) log
4
(

y
15

x
3
)
20) log
2

u
5

v
5
21) log
3

zyx
22) ln

x
6

y
3
23)

2

X

Z 24)

Y + 2

Z 25)

B 3

A 26)

X +

Z 2

Y
1 F2Q0x1329 fKvuQt2a3 vSAoofitswiaBr3en OLpLFCv.H m bAplHlB xr5iBgphRtVsA hroeGsveMrzvlecdi.U M xMUa8dKe5 YwsiothhM WIJ nGf7ixnDiwtVe6 tAslsgpesbgrda1 820.h Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 4
Name___________________________________
Date________________
I H240s1B2K tK6uEtDae kSQoEfEtdwea1rGeE TLqLZCc.c h kAll2l7 Zr3iegehytqs2 7rbe9s3eQrhv0e9d8.G
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log

n

m = 16 2) log

m
114 =

n
Rewrite each equation in logarithmic form.
3)

u
15
=

v 4)

y

x
= 36
Evaluate each expression.
5) log
3
27 6) log
6
36
7) log
2
8 8) log
3
81
9) log
36

1
6
10) log
4
64
11) log
3

1
243
12) log
7
49
13) log
2

1
64
14) log
2
32
Expand each logarithm.
15) log
2
(

c
3
3

a
)
16) log
9
(

x

y

z
6
)
17) log
9

(

u
4


v
)
5
18) log
3
(

x

y

z
4
)
Condense each expression to a single logarithm.
19)

3log
6

z +

log
6

x
2
20)

5log
7

x

30log
7

y
21)

3log
8

c +

log
8

a
2
22)

30ln

a +

5ln

b
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
6
9 =

X
log
6
8 =

Y
log
6
10 =

Z
Find log
6

10
81
24) log
9
4 =

X
log
9
7 =

Y
log
9
6 =

Z
Find log
9
196
25) log
3
7 =

A
log
3
10 =

B
log
3
4 =

C
Find log
3
1960
26) log
6
10 =

X
log
6
9 =

Y
log
6
4 =

Z
Find log
6

1
400
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Answers to Worksheet: Logarithmic Functions (ID: 4)
1)

n
16
=

m 2)

m

n
= 114
3) log

u

v = 15 4) log

y
36 =

x
5) 3 6) 2 7) 3 8) 4
9)

1
2
10) 3 11) 5 12) 2
13) 6 14) 5
15)

3log
2

c +

log
2

a
3
16)

log
9

x + log
9

y +

6log
9

z 17)

20log
9

u +

5log
9

v 18)

log
3

x + log
3

y +

4log
3

z
19) log
6
(

z
3

x
)
20) log
7

x
5

y
30
21) log
8
(

c
3

a
)
22) ln
(

b
5

a
30
)
23)

Z 2

X 24)

2

Y +

X 25)

B +

C + 2

A 26)

2

X

Z
U j2y0g1f2C YKYu0t1a9 2SfoFfLtLwOaKrFem hLjL6C2.K X iA2lKlJ 9rMisgRhdt0sI 0rReMseeXr2v4eJ dy.k U hMVaMdde1 4wMintMh7 yIOnXf8iYnBiRtaeF 7ASlKgneGbGrAam i2b.1 Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 5
Name___________________________________
Date________________
c Q2z0u142h J Kpubt2aK nSRovfbt2wcavr6em DLsLTCs.h 3 sAGlolX qrFiegah1txsZ Vr4ewsResrSvHeTda.v
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log

11
7

a =

b 2) log

v
89 =

u
Rewrite each equation in logarithmic form.
3)

y
2
=

x 4)

x

y
= 80
Evaluate each expression.
5) log
2
4 6) log
4
16
7) log
6

1
216
8) log
3

1
27
9) log
4
64
10) log

1
2

1
64
11) log
7
343 12) log
27
3
13) log
3

1
81
14) log
5
25
Expand each logarithm.
15) log
(

u
3

v
2
)
16) log
9

a
2

b
3
17) log
7
3

x

y

z
18) log
8

(

x

y
4
)
5
Condense each expression to a single logarithm.
19)

log
5

x
2
+

log
5

y
2
+

log
5

z
2
20)

5log
6

u +

20log
6

v
21)

2log
5

a +

4log
5

b 22)

2log
4

u +

8log
4

v
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
8
10 =

M
log
8
6 =

P
log
8
7 =

Q
Find log
8
420
24) log
8
12 =

R
log
8
11 =

S
log
8
10 =

T
Find log
8

10
121
25) log
8
12 =

M
log
8
11 =

P
log
8
9 =

Q
Find log
8

363
4
26) log
7
12 =

M
log
7
10 =

P
log
7
8 =

Q
Find log
7

200
3
l K2r0n1X2h PKquptoas mSpoifQtMweamrfeH 0LhLWCD.g u VAzlslH irqiBgyh8tCsR tr5eusZearivXeldY.e u AMAaadoef xwJ ist3hL oIsnnfFiYnqi0tFe8 WAQlugAeabJ rzaa W2U.c Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 5)
1)

(

11
7
)

b
=

a
2)

v

u
= 89
3) log

y

x = 2 4) log

x
80 =

y
5) 2 6) 2 7) 3 8) 3
9) 3 10) 6 11) 3
12)

1
3
13) 4 14) 2 15)

3log

u +

2log

v 16)

2log
9

a

3log
9

b
17)

log
7

x
3
+

log
7

y
3
+

log
7

z
3
18)

5log
8

x +

20log
8

y
19) log
5

zyx
20) log
6
(

v
20

u
5
)
21) log
5
(

b
4

a
2
)
22) log
4
(

v
8

u
2
)
23)

Q +

P +

M
24)

T 2

S 25)

Q + 2

P

M 26)

Q + 2

P

M
m c2v0g1Z26 hKJ ultHat gSToXf6towsaTrcel iLwLJ CT.i S hAfldl8 Vr8iEgHhtt1sg Br6ewsJ eYrovZeVdq.X l eM5and5ed OwYixtKhr gItn8fpixnMiBtiet zASlqgLeHbNr7aj h2w.u Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 6
Name___________________________________
Date________________
b O2l0w1I 23 LKru6tI a1 KSI oKfdtNwxaCrNeP eLsLSCG.7 N 7AylHlp uroiFgAh1tOs4 Rr8eVsgeFrxvfeqdc.c
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log
2
64 = 6
2) log
19

1
361
= 2
Rewrite each equation in logarithmic form.
3)

16
2
= 256 4)

y
2
=

x
Evaluate each expression.
5) log
4
64 6) log
2
16
7) log
7
49 8) log
9
3
9) log
4

1
16
10) log
6
216
11) log
4
16
12) log
6

1
36
13) log

1
7

1
343
14) log
2
32
Expand each logarithm.
15) log
7
(

x

y

z
3
)
16) log
6
(

w
5
3

u
)
17) log
6

(

a
6


b
)
2
18) log
5

(

x

y
3 )
5
Condense each expression to a single logarithm.
19)

5log
4

z +

log
4

x
3
20)

2log
3

x

6log
3

y
21)

10log
4

a +

5log
4

b
22)

log
2

z +

log
2

x
3
+

log
2

y
3
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
6
8 =

R
log
6
11 =

S
log
6
10 =

T
Find log
6

11
80
24) log
3
7 =

X
log
3
8 =

Y
log
3
10 =

Z
Find log
3

7
100
25) log
6
4 =

A
log
6
11 =

B
log
6
10 =

C
Find log
6

242
5
26) log
3
4 =

A
log
3
10 =

B
log
3
11 =

C
Find log
3
4000
c Q20001D2F oK6uNt5af rScogfmtZwcaUrYez 7L1LoCq.3 A 6AllVlx 9rdikgsh9tBsd 3rReUsZewr0v7e9dt.j 7 gMPaFdqec Ww9i7t2hd 7IBnofpiDni iftieg 6A7lRgteXbPrRaq D2v.B Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 6)
1)

2
6
= 64
2)

19
2
=

1
361
3) log
16
256 = 2 4) log

y

x = 2
5) 3 6) 4 7) 2
8)

1
2
9) 2 10) 3 11) 2 12) 2
13) 3 14) 5 15)

log
7

x + log
7

y +

3log
7

z
16)

5log
6

w +

log
6

u
3
17)

12log
6

a +

2log
6

b 18)

5log
5

x

15log
5

y
19) log
4
(

z
5
3

x
)
20) log
3

x
2

y
6
21) log
4
(

b
5

a
10
) 22) log
2
(

z
3

yx
)
23)

S

T

R 24)

X 2

Z 25)

A + 2

B

C 26)

A + 3

B
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Math IV - Advanced Algebra and Trigonometry
ID: 7
Name___________________________________
Date________________
b u2l0a182G XKQuKtraD MSLoGfqtvwvaSrGea CLALOCk.v Q dAWljlk dr2isgghMtlsi PrQeHsyenrGv5e4dz.L
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log
5
25 = 2
2) log
64
2 =

1
6
Rewrite each equation in logarithmic form.
3)

9
2
= 81 4)

11
0
= 1
Evaluate each expression.
5) log
3
243 6) log
36
6
7) log
7
49 8) log
125
5
9) log
6
36 10) log
2
4
11) log
2
8 12) log
4
16
13) log
64

1
2
14) log
4
64
Expand each logarithm.
15) log
3
(

u
4

v
5
) 16) log
4
3

x

y

z
17) log
2

(

a

b
6
)
2
18) log
4

(

x

y
6
)
3
Condense each expression to a single logarithm.
19)

12log
8

a

4log
8

b
20)

log
2

x
3
+

log
2

y
3
+

log
2

z
3
21)

4log
9

u +

2log
9

v
22)

log
8

x
3
+

log
8

y
3
+

log
8

z
3
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
7
12 =

U
log
7
10 =

V
log
7
8 =

W
Find log
7
800
24) log12 =

U
log8 =

V
log7 =

W
Find log

16
3
25) log
5
12 =

A
log
5
9 =

B
log
5
7 =

C
Find log
5

343
9
26) log
7
10 =

R
log
7
6 =

S
log
7
11 =

T
Find log
7

1
660
8 I 240k1k2Q KKlustCaM USLoqfytHwDa1r6eS CLtLXCa.2 P KAclNlz YrOiI gdhjtWse 0rdecsxebrQvMe0d6.L r 8MOacdzeJ uweizt7hA MI0n2f7iVnai6t4e1 oAolagtexbHr0ae P2f.F Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 7)
1)

5
2
= 25
2)

64

1
6
= 2
3) log
9
81 = 2 4) log
11
1 = 0
5) 5
6)

1
2
7) 2
8)

1
3
9) 2 10) 2 11) 3 12) 2
13)

1
6
14) 3 15)

4log
3

u +

5log
3

v
16)

log
4

x
3
+

log
4

y
3
+

log
4

z
3
17)

2log
2

a +

12log
2

b 18)

3log
4

x +

18log
4

y
19) log
8

a
12

b
4
20) log
2
3

zyx 21) log
9
(

v
2

u
4
) 22) log
8
3

zyx
23)

2

V +

W 24)

2

V

U 25)

3

C

B 26)

R

S

T
i 62y0S1B2Y XKMu6txaB fSMo5f5tuwGaNrneD uLALI Cz.y I 0AnlGlm WrfisgGhNt7sa I r4eRsOeWrMvKeNd4.b H rMGaVdgeX 2wfibtEhD AIinrfMiRnliCtaei 2ADlEgMecb0rsa3 W2T.I Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 8
Name___________________________________
Date________________
0 N2Y0n1z2n UKzuNtfaD J ScohfdtSwoaTrUeF RLWLCCS.h X 9ABl5lr XrziTgNhRtnsy Yryehswef ravAefdm.A
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log
6
216 = 3 2) log
16
256 = 2
Rewrite each equation in logarithmic form.
3)

400

1
2
= 20
4)

4
2
=

1
16
Evaluate each expression.
5) log
49
7 6) log
4
64
7) log
2
4 8) log
3
9
9) log

1
7

1
343
10) log
3
81
11) log
5

1
125
12) log
5
1
13) log
36
6 14) log
2
32
Expand each logarithm.
15) log
9
(

z
3

x

y
)
16) log
2

(

u
3


v
)
5
17) log

(

a
6


b
)
3
18) log
9

(

x

y
5 )
2
Condense each expression to a single logarithm.
19)

4log
5

a

8log
5

b 20)

5log
7

a

10log
7

b
21)

log
6

z +

log
6

x
3
+

log
6

y
3
22)

30log
6

u +

5log
6

v
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
9
4 =

A
log
9
10 =

B
log
9
7 =

C
Find log
9

1
25
24) log
8
6 =

U
log
8
7 =

V
log
8
10 =

W
Find log
8

35
3
25) log
5
11 =

A
log
5
12 =

B
log
5
8 =

C
Find log
5

33
16
26) log
9
8 =

A
log
9
10 =

B
log
9
12 =

C
Find log
9

1
125
u f2X0M1w2D 0Kiu4tPaq 8S4oWf9tOweaSrjeS j LtLRC3.j k J AI lulu lrJ iTgehHtVsJ arceSsLeQrqvveKdA.O R EMzawdDez OwFi5tahG QIsnVf5iVnKiMtPeO PA2logkexb0rVar 62e.R Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 8)
1)

6
3
= 216 2)

16
2
= 256
3) log
400
20 =

1
2
4) log
4

1
16
= 2
5)

1
2
6) 3 7) 2 8) 2
9) 3 10) 4 11) 3 12) 0
13)

1
2
14) 5
15)

log
9

z +

log
9

x
3
+

log
9

y
3
16)

15log
2

u +

5log
2

v 17)

18log

a +

3log

b 18)

2log
9

x

10log
9

y
19) log
5

a
4

b
8
20) log
7

a
5

b
10
21) log
6
(

z
3

yx
)
22) log
6
(

v
5

u
30
)
23)

A 2

B 24)

W +

V

U 25)

B +

A 2

C 26)

A 3

B
e J 2p031M2v 9Kzu1ttaF tSDoffhtFwjafrUeM oLnL5C2.H p XA4lSl9 iruiTgEhXtHsq arseBsJ earQv4eGdf.2 a sM9axdAeU mw9iFtVh2 OI9nTfximnMimt9eJ J ARlQg0eYbcr5aJ o2C.z Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 9
Name___________________________________
Date________________
z 92a0v1C2D XKcuLtma3 3SHo1fVtfwoaCrsem sL0LuCY.H 9 cAAlolk kr8iFgnhI tZsG qr2e1sFeRr4vCegdW.g
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log
18
324 = 2 2) log
2
8 = 3
Rewrite each equation in logarithmic form.
3)

13
2
= 169 4)

15
2
= 225
Evaluate each expression.
5) log
2
8
6) log
3

1
27
7) log
3
243
8) log
4

1
64
9) log
2
4
10) log
125

1
5
11) log
2

1
4
12) log
4
16
13) log
6

1
216
14) log
8
2
Expand each logarithm.
15) log
6
3

x

y

z 16) log
7
(

a
6

b
5
)
17) log
7

(

u
3

v
)
4
18) log
8

x

y

z
Condense each expression to a single logarithm.
19)

log
4

x + log
4

y +

2log
4

z 20)

10log
5

u

2log
5

v
21)

3log
5

x +

4log
5

y 22)

3log
3

x +

2log
3

y
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log6 =

X
log11 =

Y
log9 =

Z
Find log

11
36
24) log12 =

A
log8 =

B
log11 =

C
Find log

3
22
25) log
8
12 =

R
log
8
7 =

S
log
8
10 =

T
Find log
8

1
343
26) log
4
11 =

X
log
4
10 =

Y
log
4
6 =

Z
Find log
4

1331
6
e P2h0Z132Z J KVuktcaB WSaoZfztSwOaYrDen XLnLiCS.j 1 nAUlAl8 trQifgWhAtFsE HrQetsBe6rPvzerdd.4 A jMoaLdRep PwMimtYhN 8IunRf9iXnNistOeO dAcl4gve9bqrhai K2d.T Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 9)
1)

18
2
= 324 2)

2
3
= 8
3) log
13
169 = 2 4) log
15
225 = 2
5) 3 6) 3 7) 5 8) 3
9) 2
10)

1
3
11) 2 12) 2
13) 3
14)

1
3
15)

log
6

x
3
+

log
6

y
3
+

log
6

z
3
16)

6log
7

a +

5log
7

b 17)

12log
7

u

4log
7

v
18)

log
8

x
2
+

log
8

y
2
+

log
8

z
2
19) log
4
(

yx

z
2
)
20) log
5

u
10

v
2
21) log
5
(

y
4

x
3
)
22) log
3
(

y
2

x
3
)
23)

Y 2

X 24)

A

B

C 25) 3

S 26)

3

X

Z
e V2z0Z1m2V TKcu8ttai VSiocfgtswna3rwez oLpLlCu.G Z TASlul1 grWiSg4hatmss LrWeesmebrUvdeUdo.K p lMBaI dFeg 6wLiwtth7 sIanzfuiznBi8t3e8 jAHlrgDeEbfr4ae c2P.T Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 10
Name___________________________________
Date________________
M I 2E0a1O24 FKguzt5a5 eSmoBfHtgwVaurFeA 1LMLpC4.O K rAcl9lp HrgiNgMhCtns8 qrhe1spekr7v5eudD.C
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log

3
2

y =

x 2) log

m =

n
Rewrite each equation in logarithmic form.
3)

6

r
= 11 4)

14

y
=

x
Evaluate each expression.
5) log
2
4 6) log
32
2
7) log
343
7
8) log

1
3

1
9
9) log
4
4 10) log
5
125
11) log
7
49 12) log
6
216
13) log
6
36
14) log
4

1
16
Expand each logarithm.
15) log
6

(

x

y
2 )
5
16) log
5
(

z

x

y
)
17) log
4

(

a
2


b
)
5
18) log
6

(

a
5


b
)
2
Condense each expression to a single logarithm.
19)

6log
9

u

24log
9

v 20)

3log
2

x

2log
2

y
21)

2log
3

u

8log
3

v
22)

log
3

z +

log
3

x
2
+

log
3

y
2
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
9
10 =

X
log
9
6 =

Y
log
9
4 =

Z
Find log
9

5
8
24) log
7
11 =

A
log
7
6 =

B
log
7
9 =

C
Find log
7

9
121
25) log
7
10 =

A
log
7
11 =

B
log
7
12 =

C
Find log
7

1
1452
26) log
9
6 =

M
log
9
10 =

P
log
9
7 =

Q
Find log
9

6
343
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Answers to Worksheet: Logarithmic Functions (ID: 10)
1)

(

3
2
)

x
=

y
2)

10

n
=

m
3) log
6
11 =

r 4) log
14

x =

y
5) 2
6)

1
5
7)

1
3
8) 2
9) 1 10) 3 11) 2 12) 3
13) 2 14) 2 15)

5log
6

x

10log
6

y
16)

log
5

z +

log
5

x
2
+

log
5

y
2
17)

10log
4

a +

5log
4

b 18)

10log
6

a +

2log
6

b
19) log
9

u
6

v
24
20) log
2

x
3

y
2
21) log
3

u
2

v
8
22) log
3
(

z

yx
)
23)

X 2

Z 24)

C 2

A 25)

2

B

C 26)

M 3

Q
k 2250N1P2W FKxuhtRal 8SyoBf2tI w5aGr6el zL6LoCp.A S dAAlnlR I reiNgJ h1t0sp 5rqessTe1rKvI eqdU.X 5 ZMUandDeI gwHi5tfhv AI5nsf6iHnI i3tAeP lAClsgheTbZr7aL I 2r.d Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 11
Name___________________________________
Date________________
h 12B0D162P r KOuRt3aU ZSaojf4tawUaYrhec HLHLjCw.T 2 bAqlclc srViRgbhDtssm hrgefsxewr1vdeSdx.x
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log

x
200 =

y 2) log

v

u = 13
Rewrite each equation in logarithmic form.
3)

n

m
=

76
161
4)

x
19
=

y
Evaluate each expression.
5) log
4
16 6) log
2
1
7) log
7

1
49
8) log
7
343
9) log
6

1
216
10) log
5
125
11) log
5

1
125
12) log
2
8
13) log
6
36 14) log
7
1
Expand each logarithm.
15) log
4

x

y

z
16) log
3

(

a
2

b
)
2
17) log
4
(

u
5

v
2
)
18) log
2
(

x

y

z
3
)
Condense each expression to a single logarithm.
19)

8log
9

a

4log
9

b
20)

5ln

z +

ln

x
3
21)

5log
2

x +

2log
2

y 22)

log
8

u + log
8

v +

4log
8

w
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
8
5 =

A
log
8
9 =

B
log
8
6 =

C
Find log
8
125
24) log
7
5 =

M
log
7
6 =

P
log
7
4 =

Q
Find log
7
64
25) log
5
6 =

P
log
5
8 =

Q
log
5
7 =

R
Find log
5

256
3
26) log
9
6 =

R
log
9
7 =

S
log
9
8 =

T
Find log
9

32
21
L o2t0f1Z2C nKJ uitQaF bSsoaf9tew1aYrReP BLWLeC7.z L oAylQlm TrZiygahhtf sA dr7eosNeI rKvee0dT.V j rMQaXd5eC Qwkiatlh8 GI4nNfuisnTiOtEe9 HAslOgseab4r0an I 2D.j Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 11)
1)

x

y
= 200 2)

v
13
=

u
3) log

n

76
161
=

m
4) log

x

y = 19
5) 2 6) 0 7) 2 8) 3
9) 3 10) 3 11) 3 12) 3
13) 2 14) 0
15)

log
4

x
2
+

log
4

y
2
+

log
4

z
2
16)

4log
3

a

2log
3

b 17)

5log
4

u +

2log
4

v 18)

log
2

x + log
2

y +

3log
2

z
19) log
9

a
8

b
4
20) ln
(

z
5
3

x
)
21) log
2
(

y
2

x
5
)
22) log
8
(

vu

w
4
)
23) 3

A 24) 3

Q 25)

3

Q

P 26)

2

T

R

S
F H2M0z1E2C LKguctAak 2SjoBf2tiwoaArNee cLaLSC4.B u MATlXlZ Pr8i9gI hjtis8 9rweRs2eGrEvReods.S U NMwaldUej VwhirtFhu I IQnMff iXnHiAtnev YAsl1gqefber1av s2G.9 Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 12
Name___________________________________
Date________________
k M2p0J 1N2C AKNuYtpac CSBoBfJ tswYaAr7e5 0LNLJ Cs.O F jA6lulz yrbi0gMhltysS PrNe9s1e5rxv6emdu.x
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log
2
23 =

b 2) log
20

x =

y
Rewrite each equation in logarithmic form.
3)

16

b
=

a 4)

b
10
= 189
Evaluate each expression.
5) log
6

1
36
6) log
4
64
7) log

1
7

1
49
8) log
7
343
9) log
3
243
10) log
9

1
3
11) log
5
125 12) log
6
1
13) log
3
27 14) log
32
8
Expand each logarithm.
15) log
2

(

a

b
6 )
2
16) ln
(

w
3

u

v
)
17) log
8

u
4

v
2
18) log
3

(

u
4


v
)
5
Condense each expression to a single logarithm.
19)

6log

u

5log

v
20)

log
7

z +

log
7

x
2
+

log
7

y
2
21)

5log
8

a

30log
8

b 22)

2log
6

a +

12log
6

b
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
7
12 =

X
log
7
9 =

Y
log
7
5 =

Z
Find log
7
540
24) log
7
12 =

A
log
7
9 =

B
log
7
5 =

C
Find log
7

15
4
25) log
7
3 =

X
log
7
8 =

Y
log
7
10 =

Z
Find log
7

4
45
26) log
3
7 =

X
log
3
10 =

Y
log
3
4 =

Z
Find log
3

25
7
W V2k0Q1x25 vKkuWtka4 kSmoSf1t9wKapr2eJ cLWLACV.3 h rAYlAlA QrKiOgchJ tSs1 drpeqsbeBrnvReddB.d S NMTa5dGeT YwtiNtNhy bIknKfviCnCiNtEeY oAclqgrepb2r7ad Z2v.G Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 12)
1)

2

b
= 23 2)

20

y
=

x
3) log
16

a =

b 4) log

b
189 = 10
5) 2 6) 3 7) 2 8) 3
9) 5
10)

1
2
11) 3 12) 0
13) 3
14)

3
5
15)

2log
2

a

12log
2

b
16)

ln

w +

ln

u
3
+

ln

v
3
17)

4log
8

u

2log
8

v 18)

20log
3

u +

5log
3

v
19) log

u
6

v
5
20) log
7
(

z

yx
)
21) log
8

a
5

b
30
22) log
6
(

b
12

a
2
)
23)

Z +

Y +

X 24)

B +

C

A
25)

Y

Z 2

X 26)

2

Y

Z

X
5 f2B0k152j WK7uYt3a8 ZSwoKf5t7wVacrDef OLzL8CR.J k eAZl8lb lr4iCgJ hotZsH NrDeMsreWrgvaeDda.T u pM6awdyeK mwEiCtJ h7 cIVnwfziUnSiEtLee CA3lEgveQb5rQaq a2a.1 Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 13
Name___________________________________
Date________________
C l2R051F2K pK9u9tmaY iSUoBfTtLwtaprkeP 7LQLlCX.k w PAzlflE 4rYiI gkhBtmsX MrceSsveHrdv6ecdd.E
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log
8
64 = 2 2) log
6
1 = 0
Rewrite each equation in logarithmic form.
3)

17
9
=

n 4)

15
2
= 225
Evaluate each expression.
5) log
3
243 6) log
32
8
7) log
4
64 8) log
5
125
9) log
7
49
10) log

1
3

1
27
11) log
9
3 12) log
6
36
13) log
16
2 14) log
64
4
Expand each logarithm.
15) log
9
(

x

y

z
5
)
16) log
7

(

u
4

v
)
2
17) log
8
(

x
2

y
5
)
18) log
7
(

x

y

z
5
)
Condense each expression to a single logarithm.
19)

4log
4

z +

log
4

x
2
20)

2log
6

x +

4log
6

y
21)

8log
5

u

2log
5

v 22)

log
5

a + log
5

b +

6log
5

c
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
9
11 =

A
log
9
10 =

B
log
9
8 =

C
Find log
9

11
64
24) log
5
12 =

P
log
5
8 =

Q
log
5
9 =

R
Find log
5

9
64
25) log
6
10 =

A
log
6
4 =

B
log
6
9 =

C
Find log
6
10000
26) log11 =

X
log9 =

Y
log12 =

Z
Find log8019
x Q2o0A1V2Q mKauZt0aj NSmodfpthwTairMeB zLELyCV.7 A uAslI l8 urfijgThktusQ 7rPeDsAetruvPeNdC.D G KMwaod6ed OwZiWt4hp UInncfKidnZi9t4e1 TAOlmgseebPrga4 Y2T.4 Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 13)
1)

8
2
= 64 2)

6
0
= 1
3) log
17

n = 9 4) log
15
225 = 2
5) 5
6)

3
5
7) 3 8) 3
9) 2 10) 3
11)

1
2
12) 2
13)

1
4
14)

1
3
15)

log
9

x + log
9

y +

5log
9

z
16)

8log
7

u

2log
7

v 17)

2log
8

x +

5log
8

y 18)

log
7

x + log
7

y +

5log
7

z
19) log
4
(

z
4

x
)
20) log
6
(

y
4

x
2
)
21) log
5

u
8

v
2
22) log
5
(

ba

c
6
)
23)

A 2

C 24)

R 2

Q 25) 4

A 26)

3

Y +

X
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Math IV - Advanced Algebra and Trigonometry
ID: 14
Name___________________________________
Date________________
t c2b0F1m2T wK3u7tba7 dSpoQf7tJ w6aer2e3 RL4L5CJ .0 U dAilOl5 Qr7iugwhjtjsi I rje8sqeurxvYeGdf .e
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log
27
3 =

1
3
2) log
14

1
196
= 2
Rewrite each equation in logarithmic form.
3)

7
0
= 1 4)

5
4
= 625
Evaluate each expression.
5) log
6
216 6) log
81
3
7) log
36
6 8) log
4
64
9) log
4
16 10) log
2
1
11) log
5

1
125
12) log
7
49
13) log
5
125
14) log
2

1
8
Expand each logarithm.
15) log
5

x
6

y
5
16) log
5
(

z
3

x

y
)
17) log
6

(

u

v
3 )
5
18) log
7

a
6

b
2
Condense each expression to a single logarithm.
19)

4log
2

u +

20log
2

v
20)

log
3

z +

log
3

x
3
+

log
3

y
3
21)

2log
4

u +

6log
4

v 22)

4log
3

x

2log
3

y
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
8
7 =

R
log
8
10 =

S
log
8
6 =

T
Find log
8

6
49
24) log12 =

M
log9 =

P
log7 =

Q
Find log567
25) log
9
8 =

P
log
9
6 =

Q
log
9
10 =

R
Find log
9

1
384
26) log
7
10 =

X
log
7
6 =

Y
log
7
9 =

Z
Find log
7
40
2 w2t0i1b2I YKGuctOaK oSAo1fztxwca9rrem NLNL8C1.u w 6AklelU broi4g9hytNsZ Hr1eFslehrCvSeRdM.8 K lM1aXdye8 RwfiUtRhi 3I0nVfeiqnyi7teed BAwlfgEefbyrhav L2R.S Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 14)
1)

27

1
3
= 3
2)

14
2
=

1
196
3) log
7
1 = 0 4) log
5
625 = 4
5) 3
6)

1
4
7)

1
2
8) 3
9) 2 10) 0 11) 3 12) 2
13) 3 14) 3 15)

6log
5

x

5log
5

y
16)

log
5

z +

log
5

x
3
+

log
5

y
3
17)

5log
6

u

15log
6

v 18)

6log
7

a

2log
7

b
19) log
2
(

v
20

u
4
) 20) log
3
(

z
3

yx
)
21) log
4
(

v
6

u
2
)
22) log
3

x
4

y
2
23)

T 2

R 24)

Q + 2

P 25)

2

P

Q 26)

X + 2

Y

Z
A d2T0l1t2i 1KhuZtCaX NSxoyfytowNaSrUer 5LxL8C7.r H jANlxlQ 1rDi1gvhbtssD Tr5eysje2ravXeydZ.Z w 1MuaBdZes 5wAiotVhJ UIUnyf0icnmiLt2eI GAQlGgfeMbWr1an V2T.b Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 15
Name___________________________________
Date________________
6 T2x0U1M2w 3KWuetRah DSUoMfVtowRayrweh kLFLKCw.G b lAblolB urr ivgi hgtysK Nrfe1slesrqvNeOd8.z
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log

1
15

1
225
= 2 2) log
18

1
324
= 2
Rewrite each equation in logarithmic form.
3)

5
4
=

1
625
4)

3
2
= 9
Evaluate each expression.
5) log
4

1
16
6) log
6

1
216
7) log
16

1
4
8) log
5
125
9) log
2
32 10) log
3
81
11) log
3
1 12) log
2
4
13) log
36

1
6
14) log
7
343
Expand each logarithm.
15) log
2
(

z
4
3

x
)
16) log
2

(

a
3

b
)
4
17) log
4

(

a
6

b
)
5
18) log
3
(

u

v

w
2
)
Condense each expression to a single logarithm.
19)

log
7

u + log
7

v +

5log
7

w 20)

18log
8

x +

6log
8

y
21)

ln

u + ln

v +

5ln

w
22)

2ln

z +

ln

x
3
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
3
11 =

A
log
3
4 =

B
log
3
10 =

C
Find log
3

121
4
24) log
7
9 =

A
log
7
10 =

B
log
7
4 =

C
Find log
7
25
25) log
4
6 =

R
log
4
9 =

S
log
4
11 =

T
Find log
4
2376
26) log
8
10 =

M
log
8
12 =

P
log
8
9 =

Q
Find log
8

5
8
L X2T0R1F2O LKtu1tEan RSEomfxtkwmazrjeq TLfLaCx.5 k rA5l6lv ir6i4gchttbsF lrTeOsueirOvbe7ds.p x QMMawd2eo YwEittBhR wISnZfRiMn6i4tref GAgl7gFe5b6rhao f2K.L Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 15)
1)

(

1
15
)
2
=

1
225
2)

18
2
=

1
324
3) log
5

1
625
= 4
4) log
3
9 = 2
5) 2 6) 3
7)

1
2
8) 3
9) 5 10) 4 11) 0 12) 2
13)

1
2
14) 3
15)

4log
2

z +

log
2

x
3
16)

12log
2

a

4log
2

b
17)

30log
4

a

5log
4

b 18)

log
3

u + log
3

v +

2log
3

w
19) log
7
(

vu

w
5
)
20) log
8
(

y
6

x
18
)
21) ln
(

vu

w
5
)
22) ln
(

z
2
3

x
)
23)

2

A

B
24)

2

B

C 25)

T + 3

R 26)

Q +

M 2

P
I 72T0R1I 2l lKHuEtTat 4Soo9fUtNwQa8raeE HLnLr Cs.X w I AJ lglT fr9iZgVhutdsJ I r0eI s4emrI vHeTdL.T E mMda2dVeX xwNiWtFh8 OImnI f0iVnZimt3eb J A3lPgceKb7r9aD h28.r Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 16
Name___________________________________
Date________________
y C2Z0p192Q 6KUuTtbad RSoojfQt5w3anrweC XLJ LSC5.k H wAllHlw 8r8izg5hwtss9 FrDeDsqeI r9vxeSdq.J
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log
17
289 = 2 2) log
7
343 = 3
Rewrite each equation in logarithmic form.
3)

(

1
14
)
0
= 1
4)

11
2
= 121
Evaluate each expression.
5) log
2
16 6) log
5
125
7) log
3
243 8) log
5
25
9) log
16
4
10) log
2

1
16
11) log
7
49 12) log
2
32
13) log
6
36 14) log
6
216
Expand each logarithm.
15) log
6

(

a

b
2
)
2
16) log

a
4

b
6
17) log
6
3

u

v

w
18) log
7

x
6

y
4
Condense each expression to a single logarithm.
19)

2ln

a +

6ln

b 20)

6log
4

x +

12log
4

y
21)

3log
2

x +

15log
2

y
22)

log
4

u
3
+

log
4

v
3
+

log
4

w
3
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
5
6 =

X
log
5
11 =

Y
log
5
4 =

Z
Find log
5

11
24
24) log
3
10 =

U
log
3
11 =

V
log
3
8 =

W
Find log
3
1100
25) log
3
10 =

A
log
3
11 =

B
log
3
8 =

C
Find log
3

11
640
26) log
8
9 =

A
log
8
12 =

B
log
8
7 =

C
Find log
8

7
16
6 V2x0V1j29 PKsuStVaH cSFoifpt0whanr6ey FL2LmC3.N I DAmlkl6 TrWiqgthLtMsE rrXe4s1eDrOvUe5dE.k i I Mqaedqe9 gwRiotWhh 6Iqn0fKiKnyiptieX 3AilvgreZbhriaM C2J .r Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 16)
1)

17
2
= 289 2)

7
3
= 343
3) log

1
14
1 = 0 4) log
11
121 = 2
5) 4 6) 3 7) 5 8) 2
9)

1
2
10) 4 11) 2 12) 5
13) 2 14) 3 15)

2log
6

a +

4log
6

b 16)

4log

a

6log

b
17)

log
6

u
3
+

log
6

v
3
+

log
6

w
3
18)

6log
7

x

4log
7

y
19) ln
(

b
6

a
2
)
20) log
4
(

y
12

x
6
)
21) log
2
(

y
15

x
3
) 22) log
4
3

wvu
23)

Y

Z

X
24)

V + 2

U 25)

B

A 2

C 26)

A +

C 2

B
o O2p071w2I dK6uitza9 YSDojfMt3wFaOriel hLBLKCZ.2 I zAI lalL 9r1i1gNhytSsX nrveQspeSrZvaeNdX.y t 6MtaKdhe1 Fw3i4tDhH aIonhfEi5nLijtYeE HARlLgvewbSrqaB N22.t Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 17
Name___________________________________
Date________________
S 52f0I 1I 2D UKnu3tBak bS1o5fRtEwKaDrQeb eLELaC5.9 h NAnlZl0 priiI guhptKsM lrhepsUef rI vWeUdE.b
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log
13
169 = 2
2) log
16
4 =

1
2
Rewrite each equation in logarithmic form.
3)

8
2
= 64 4)

10
3
= 1000
Evaluate each expression.
5) log
5
125 6) log
25
5
7) log
6
36 8) log
7
49
9) log
3
81 10) log
4
64
11) log
3
9
12) log
7

1
49
13) log
2

1
8
14) log
2
64
Expand each logarithm.
15) log
3

(

a

b
2 )
6
16) log

(

x
3


y
)
6
17) log
2
(

w
3
3

u
)
18) log
2

(

x
5


y
)
6
Condense each expression to a single logarithm.
19)

8log
8

x +

4log
8

y
20)

6log
8

w +

log
8

u
3
21)

4log
9

x

16log
9

y 22)

4log

u

24log

v
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
7
12 =

U
log
7
8 =

V
log
7
9 =

W
Find log
7

4
27
24) log
7
12 =

R
log
7
8 =

S
log
7
9 =

T
Find log
7

81
8
25) log
3
8 =

M
log
3
10 =

P
log
3
7 =

Q
Find log
3

100
49
26) log
6
10 =

A
log
6
8 =

B
log
6
9 =

C
Find log
6

225
2
j 42W0E1Y2o 2KyuVtMaO gS9oFfgtcwFaprOeQ TL4L8C8.O 6 bAnlVlE DryiDgMh7tKsW PrseVsOeyrjvPeadi.M q I MDaEdMe8 OwYiJ t0hU CIOn9fHiSn8iqtuey 3AVlNgeePb7rpat u28.B Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 17)
1)

13
2
= 169
2)

16

1
2
= 4
3) log
8
64 = 2 4) log1000 = 3
5) 3
6)

1
2
7) 2 8) 2
9) 4 10) 3 11) 2 12) 2
13) 3 14) 6 15)

6log
3

a

12log
3

b 16)

18log

x +

6log

y
17)

3log
2

w +

log
2

u
3
18)

30log
2

x +

6log
2

y
19) log
8
(

y
4

x
8
)
20) log
8
(

w
6
3

u
)
21) log
9

x
4

y
16
22) log

u
4

v
24
23)

U 2

W
24)

2

T

S 25)

2

P 2

Q 26)

C + 2

A

B
7 b2w0b1M2m eKAu1tua6 PSqoqfVtxw0aNrUep pLNLpCb.j N fAUlKlJ BrCiXgXhI tksy Xrqe3sve2r4vEeEd7.O e DM8aI dleK 5wciRtAha oI5nRfCiJ nFidtI ei gAulQgTeUbdrzaL S2d.q Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 18
Name___________________________________
Date________________
K B2J 081t2H xKEuitCa7 DS1ojfwtlwha7rkeh 3LOLiC2.8 b gARlTlZ OrXixgohatcs0 I ryeQsne4rfvoe5dh.J
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log

b
150 =

a 2) log

v
22 =

u
Rewrite each equation in logarithmic form.
3)

16
2
= 256 4)

12

m
=

n
Evaluate each expression.
5) log
6
216 6) log
4
16
7) log
4
64
8) log
3

1
27
9) log
2
4 10) log
2
32
11) log
3
27 12) log
5
25
13) log
7
343 14) log
6
36
Expand each logarithm.
15) log
9
(

x
3

y
4
)
16) log
9

(

x

y
4
)
4
17) log
7
(

u
5

v
3
) 18) log
8
3

a

b

c
Condense each expression to a single logarithm.
19)

5log
5

u +

6log
5

v 20)

6log
4

x

3log
4

y
21)

12log
7

x

6log
7

y
22)

log
6

a
3
+

log
6

b
3
+

log
6

c
3
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
3
8 =

X
log
3
10 =

Y
log
3
11 =

Z
Find log
3

11
64
24) log
3
4 =

A
log
3
10 =

B
log
3
7 =

C
Find log
3

7
100
25) log
6
11 =

R
log
6
4 =

S
log
6
10 =

T
Find log
6

40
121
26) log
6
9 =

X
log
6
10 =

Y
log
6
8 =

Z
Find log
6

256
5
4 U2z0E1F2L J KOu9t0aA 8SyodfVtLwTaerxeL 9LzLbCF.1 m vAblZl5 ErDi0g5hOtTsp I rJ ewsRewr2vdeCdZ.B x 0M9aHdEe5 twfistaht XIXnMf1i2nuiYtvel bAKlLgYe2brr3a8 N2i.q Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 18)
1)

b

a
= 150 2)

v

u
= 22
3) log
16
256 = 2 4) log
12

n =

m
5) 3 6) 2 7) 3 8) 3
9) 2 10) 5 11) 3 12) 2
13) 3 14) 2 15)

3log
9

x +

4log
9

y
16)

4log
9

x +

16log
9

y 17)

5log
7

u +

3log
7

v
18)

log
8

a
3
+

log
8

b
3
+

log
8

c
3
19) log
5
(

v
6

u
5
)
20) log
4

x
6

y
3
21) log
7

x
12

y
6
22) log
6
3

cba
23)

Z 2

X 24)

C 2

B 25)

S +

T 2

R 26)

3

Z

Y
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Math IV - Advanced Algebra and Trigonometry
ID: 19
Name___________________________________
Date________________
h g2K0Z1f28 wK8uDtlat yS3oNfMt5wdayrUeh 0LhLKCQ.J v 2AI lilI urMiDgzhCtxsy crXejsMeYrpvBeHdL.y
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log

y

x = 7 2) log

x
11 = 11
Rewrite each equation in logarithmic form.
3)

2

y
=

x 4)

y

x
= 67
Evaluate each expression.
5) log
6

1
216
6) log
7

1
343
7) log
4

1
4
8) log
7
343
9) log
16
4 10) log
25
5
11) log
2
32
12) log
2

1
16
13) log
7

1
49
14) log
6

1
36
Expand each logarithm.
15) log
7

(

u

v
4 )
4
16) log
6

(

x
4


y
)
4
17) log
7
(

c
2
3

a
)
18) log
5

(

x

y
6 )
6
Condense each expression to a single logarithm.
19)

4log
3

x

24log
3

y 20)

24log
4

u +

6log
4

v
21)

log
5

c +

log
5

a
3
+

log
5

b
3
22)

ln

c +

ln

a
2
+

ln

b
2
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
5
6 =

M
log
5
4 =

P
log
5
11 =

Q
Find log
5
726
24) log
8
6 =

A
log
8
10 =

B
log
8
7 =

C
Find log
8
1000
25) log
5
6 =

R
log
5
8 =

S
log
5
9 =

T
Find log
5

2
243
26) log
9
7 =

R
log
9
12 =

S
log
9
10 =

T
Find log
9

35
72
k 72Q0Z1d2e HKYubtPaW HSdoBfttlwHaLrPeW wLI LiCf.K G aAQlclq FrWiSgMh9tasJ yrXessCe3rivAeadb.I B BM2awdf et GwkiytAhC aIDnsfDipnsiGtze1 J A4lwgDeiburuaC B21.h Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 19)
1)

y
7
=

x 2)

x
11
= 11
3) log
2

x =

y 4) log

y
67 =

x
5) 3 6) 3 7) 1 8) 3
9)

1
2
10)

1
2
11) 5 12) 4
13) 2 14) 2 15)

4log
7

u

16log
7

v
16)

16log
6

x +

4log
6

y
17)

2log
7

c +

log
7

a
3
18)

6log
5

x

36log
5

y
19) log
3

x
4

y
24
20) log
4
(

v
6

u
24
) 21) log
5
(

c
3

ba) 22) ln(

c

ba)
23)

2

Q +

M 24) 3

B 25)

R 3

T 26)

T +

R 2

S
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Math IV - Advanced Algebra and Trigonometry
ID: 20
Name___________________________________
Date________________
l P230n1K26 VK2ubtrau wSxoPfCtNw1aPrSeq iLqL7CF.X O oAolxl9 RrmiKgKh3tbsy GrEeHsWeJ rtvmeSdf.c
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log

y
147 =

x 2) log
7

x = 3
Rewrite each equation in logarithmic form.
3)

(

5
8
)

x
=

y
4)

m
5
=

n
Evaluate each expression.
5) log
7

1
49
6) log
2

1
4
7) log
5
25
8) log
4

1
16
9) log
7
343 10) log
7
7
11) log
6

1
216
12) log
2
64
13) log
3
9 14) log
4
16
Expand each logarithm.
15) log
4

u

v

w
16) log
5

(

x
3

y
)
4
17) log
3

(

x
4

y
)
3
18) log
(

x
2

y
3
)
Condense each expression to a single logarithm.
19)

log
2

x + log
2

y +

5log
2

z 20)

24log
9

x

6log
9

y
21)

2log
9

a +

3log
9

b 22)

log
8

x + log
8

y +

2log
8

z
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
5
12 =

A
log
5
11 =

B
log
5
8 =

C
Find log
5

2
33
24) log
9
5 =

X
log
9
6 =

Y
log
9
8 =

Z
Find log
9

3
20
25) log8 =

R
log9 =

S
log6 =

T
Find log

81
64
26) log
7
4 =

X
log
7
9 =

Y
log
7
6 =

Z
Find log
7

8
27
H Y2F0A1e29 aKsuHtUaf NSvoBf8tqwCaarBer ML9LoCt.G P WADlmlp 2rkidgAhKthsO prwetsFe7ryvxeZdP.q l SM8aSdUeD Nw6iRtNhW YIYn2fci6nzilt7eu sASl7gWetbNr6ai a2P.l Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 20)
1)

y

x
= 147 2)

7
3
=

x
3) log

5
8

y =

x 4) log

m

n = 5
5) 2 6) 2 7) 2 8) 2
9) 3 10) 1 11) 3 12) 6
13) 2 14) 2
15)

log
4

u
2
+

log
4

v
2
+

log
4

w
2
16)

12log
5

x

4log
5

y 17)

12log
3

x

3log
3

y 18)

2log

x +

3log

y
19) log
2
(

yx

z
5
)
20) log
9

x
24

y
6
21) log
9
(

b
3

a
2
)
22) log
8
(

yx

z
2
)
23)

C

B

A 24)

Y

Z

X 25)

2

S 2

R 26)

2

X

Y

Z
Y O2j0M1Y2X CKkuYtTa7 FSboof2tgwSa9rweo ML8LKCq.f m 0AJ lnlU yrtiNg2hNtosO 8rwe1s1eKravXezd0.X t 5MRaUdEeB Fwsiutth2 cIRnYfPi1nViAtvee 9AHlqgOeqb3rMaL p2z.3 Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 21
Name___________________________________
Date________________
M 52j0y1P2T cKfuDtxa9 vSPo2fitPw6aJ rmeM tL9LqCy.T i XAslylO XrXihgmh0thsN J rle8svesrLvZerdj.k
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log

r
8 = 5 2) log

x

y = 20
Rewrite each equation in logarithmic form.
3)

m
6
= 132
4)

(

2
3
)
14
=

x
Evaluate each expression.
5) log
6
36 6) log
2
16
7) log
49
7 8) log
7
49
9) log
343
7 10) log
3
81
11) log
3

1
243
12) log
4
64
13) log
6

1
36
14) log
2
32
Expand each logarithm.
15) log
8

a
6

b
4
16) log
9
(

w

u

v
)
17) log
2

(

x

y
3 )
4
18) log

(

x
5


y
)
4
Condense each expression to a single logarithm.
19)

6log
8

x

18log
8

y 20)

3log
6

a

3log
6

b
21)

log
7

z +

log
7

x
3
+

log
7

y
3
22)

5log

a +

20log

b
Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the
variables given.
23) log
3
4 =

R
log
3
10 =

S
log
3
11 =

T
Find log
3

8
5
24) log
8
9 =

P
log
8
6 =

Q
log
8
10 =

R
Find log
8

1
15
25) log
9
8 =

A
log
9
7 =

B
log
9
12 =

C
Find log
9

1
126
26) log
6
10 =

A
log
6
4 =

B
log
6
11 =

C
Find log
6

55
8
K 4240O1n2I YKKuptQa9 NSeopfstPwkajrjeF WLCLkCK.L p oAZl4lm LrsiXgShNtQsF prjensXeLrgvSendD.c T RMl aJ dAeS uwiiBtf hJ hII nLfLiZn2iZtve7 7AUlTgieYbSrmaa D2x.k Worksheet by KutaSoftwareLLC
Answers to Worksheet: Logarithmic Functions (ID: 21)
1)

r
5
= 8 2)

x
20
=

y
3) log

m
132 = 6 4) log

2
3

x = 14
5) 2 6) 4
7)

1
2
8) 2
9)

1
3
10) 4 11) 5 12) 3
13) 2 14) 5 15)

6log
8

a

4log
8

b
16)

log
9

w +

log
9

u
2
+

log
9

v
2
17)

4log
2

x

12log
2

y 18)

20log

x +

4log

y
19) log
8

x
6

y
18
20) log
6

a
3

b
3
21) log
7
(

z
3

yx
)
22) log
(

b
20

a
5
)
23)

2

R

S 24)

Q

R

P 25)

A

B 2

C 26)

A +

C 2

B
q n2d0i1O2o oKhu2t5aq OSOo3f2tHwGadrkeI KLVLaCj.Z u vAjlKlF Urti3gFhWtds8 4rye9sl ezr5vEeUdJ .c y 0M2aEdgeu bwmiutehK eIYnmfgiVnsiktceH 1AnlugjeKbErDa1 R2s.m Worksheet by KutaSoftwareLLC
Math IV - Advanced Algebra and Trigonometry
ID: 22
Name___________________________________
Date________________
Z C2m0H1J 2S 9KpuRtAap 1SToSfqtdwSaArUeU 7LZLLCu.3 s RA4lQlI greiCgShvtYsO qrEeXsMeJ rgvdeVdE.6
Worksheet: Logarithmic Functions
Rewrite each equation in exponential form.
1) log
16
256 = 2
2) log
216

1
6
=