Free Printable Logarithm Review

1.

8^3x+3 = 8⁶

a)

x=28

b)

x=3

c)

x=1

d)

x=12

2.

Solve for n:
2^-2n = 2⁶

a)

-1

b)

-7

c)

5

d)

-3

3.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

4.

solve for x.

$3^{2x-1}\cdot3^4=3$

a)

1/2

b)

5/8

c)

-1

d)

8/5

5.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

6.

Solve 8 = 2^5x+7

a)

x = ⅘

b)

x = ¼

c)

x = -⅘

d)

x = -¼

7.

Solve for b:
4^{3b - 3} = 1/16

a)

7

b)

-1/4

c)

1/2

d)

1/3

8.

Solve the following exponential equation:
$9^{8-x}=27^{x-3}$

a)

$x=5$

b)

$x=-5$

c)

$x=\frac{1}{5}$

d)

$x=-\frac{1}{5}$

9.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

10.

Write the exponential equation as a logarithm
6³=216

a)

log₆(3) = 216

b)

log₃(6) = 216

c)

log₆(216)=3

d)

log₂₁₆(6)=3

11.

Rewrite the equation into logarithmic form:

6² = 36

a)

log₆ 2 = 36

b)

log₆ 36 = 2

c)

ln 36 = 2

d)

6³⁶ = 2

12.

Write in logarithm form
$6^{-3}=\frac{1}{216}$

a)

$\log_6\ -3=\frac{1}{216}$

b)

$\log_{-3}\ 6=\frac{1}{216}$

c)

$\log_6\ \frac{1}{216}=-3$

d)

$\log_{\frac{1}{216}}\ 6=-3$

13.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

14.

Change to Exponential Form:

log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

15.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

16.

Rewrite in exponential form. $\log_{6\ }t=m$

a)

$m^t=6$

b)

$t^m=6$

c)

$6^t=m$

d)

$6^m=t$

17.

Rewrite as an exponential: $\log_93=\frac{1}{2}$

a)

$9^{\frac{1}{2}}=3$

b)

$3^{\frac{1}{2}}=9$

c)

$9^3=\frac{1}{2}$

d)

$\left(\frac{1}{2}\right)^9=3$

18.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

19.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

20.

$\log_216$

a)

8

b)

4

c)

6

21.

$\log_5625$

a)

5

b)

4

c)

25

22.

$\log_5\ \frac{1}{25}$

a)

$\frac{1}{2}$

b)

2

c)

-2

23.

$\log_{\frac{1}{3}}\ 9$

a)

$\frac{1}{3}$

b)

2

c)

-2

24.

$\log_{\frac{1}{4}}\ 16$

a)

$\frac{1}{3}$

b)

2

c)

-2

25.

Evaluate $\log_28$ .

a)

3

b)

4

c)

16

d)

64

26.

$\log_a\ a\ =$

a)

Not defined

b)

0

c)

1

d)

$a$

27.

$\log_a\ 1\ =$

a)

Not defined

b)

0

c)

1

d)

$a$

28.

$\log_{x\ }\sqrt[]{x}\ =$

a)

1

b)

2

c)

$\frac{1}{2}$

d)

x

29.

$\log_{25\ }5\ =$

a)

1

b)

25

c)

$\frac{1}{2}$

d)

5

30.

a)

b)

c)

d)

31.

Rewrite it using positive exponents $x^{-3}$

a)

$-x^3$

b)

$\frac{1}{x^3}$

c)

$\frac{1}{x^{-3}}$

d)

$-x^{-3}$

32.

a)

b)

c)

d)

33.

(t^-6)^-5

a)

t^-11

b)

t^-30

c)

t³⁰

d)

t¹¹

34.

(3xy)²

a)

9x²y²

b)

6x²y²

c)

3xy²

d)

3x²y²

35.

Simplify the expression:

$\left(k^2\right)^5$

a)

$k^7$

b)

$k^3$

c)

$k^{32}$

d)

$k^{10}$

36.

Expand: $\log_6\left(\frac{5}{4y}\right)$

a)

$\log_65\ +\ \log_64\ +\ \log_6y$

b)

$\log_65\ -\ \log_64\ +\ \log_6y$

c)

$\log_65\ -\ \log_64\ -\ \log_6y$

d)

$\log_65\ -\ \log_64y$

37.

Expand: $\log_4\left(3x^2\right)$

a)

$2\log_43x$

b)

$2\log_43\ +\ 2\log_4x$

c)

$\log_43\ +\ 2\log_4x$

d)

$2\log_43\ +\ \log_4x$

38.

Condense: $\frac{1}{2}\log_3x\ +\ 5\log_3y$

a)

$\log_3\left(\sqrt{x}y^5\right)$

b)

$\log_3\left(\sqrt{x}y^5\right)$

c)

$\log_3\left(5\sqrt{x}y\right)$

d)

$\log_3\left(xy\right)^{\frac{5}{2}}$

39.

Condense the Logarithm $5\log_{ }a\ -\ 25\log_{ }b$

a)

$\log\ \left(a^5+b^{25}\right)$

b)

$\log\ \left(a^5-b^{25}\right)$

c)

$\log\ \left(ab\right)^{25}$

d)

$\log_{ }\ \left(\frac{a^5}{b^{25}}\right)$

40.

Simplify: $\log_4\left(x+4\right)-\log_4\left(x-5\right)$

a)

$\log_49$

b)

$\log_4\left(2x-1\right)$

c)

$\log_4\left(x^2-x-20\right)$

d)

$\log_4\left(\frac{x+4}{x-5}\right)$

41.

Simplify: $2\log_3\left(11x\right)$

a)

$\log_3\left(22x\right)$

b)

$\log_3\left(121x\right)$

c)

$\log_3\left(121x^2\right)$

d)

$\log_3\left(11x^2\right)$

42.

Expand using the properties of Logaritms $\log_{ }\ \frac{x^3}{y^4z}$

a)

$\log_{ }x+4\log_{ }y\ +\log_{ }z$

b)

$3\log_{ }x-4\log_{ }y\ -\log_{ }z$

c)

$3\log_{ }x+4\log_{ }y\ +\log_{ }z$

d)

$3\log_{ }x-4\log_{ }y\ +\log_{ }z$

43.

Expand the logarithm.
$\log\frac{x}{y^6}$

a)

$\log x+6\log y$

b)

$\log x-6\log y$

c)

$\log x+\log6y$

d)

$\log x-\log6y$

44.

Write log_b(xy) as two logs

a)

log_bx+log_by

b)

log_bx-log_by

c)

log_bx*log_by

d)

log_bx/log_by

45.

Rewrite as a single logarithm:

\log_260\ -\ \log_210

a)

$\log_26$

b)

$\log_250$

c)

$\frac{\log_260}{\log_210}$

d)

$\log_270$

46.

Expand

a)

log₈x+log₈y+log₈z

b)

5log₈x+5log₈y+5log₈z

c)

log₈xy+5log₈z

d)

log₈x+log₈y+5log₈z

47.

Condense

a)

logxyz³

b)

log(xy/z³)

c)

logx+logy+logz³

d)

logx³y³z³

48.

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

49.

Write as a single log: log 12 + 2 log x

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

50.

a)

ln(wvu⁵)

b)

ln(u + v + w⁵)

c)

ln(uvw⁵)

d)

ln(uvw)⁵

Logarithm Review

Total questions: 50

Worksheet time: 3hrs 57mins

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