Free Printable Exponential and Logarithms Test Review

1.

What is the inverse of an exponential function?

a)

Exponential function

b)

Power function

c)

Logarithmic function

d)

Base e function

2.

Write in exponential form.

log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

3.

Write in exponential form.

log₂(¹/₈) = -3

a)

2^-3 = ¹/₈

b)

2^1/8= -3

c)

-3² = ¹/₈

d)

-3^1/8 = 2

4.

Write in logarithmic form.

2^-4 = ¹/₁₆

a)

log₂(¹/₁₆) = -4

b)

log_-4(¹/₁₆) = 2

c)

log_-4 2 = ¹/₁₆

d)

log₂(-4) = ¹/₁₆

5.

Write in logarithmic form.

5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₅25 = 2

d)

log₂₅5 = 2

6.

Solve for x using the same base method:

(-3)^x = (-3)¹³

a)

-3

b)

13

c)

X+13

d)

x-13

7.

Solve for x using the same base metod:

27^2x = 3^x-7

a)

$-\frac{7}{3}$

b)

-1

c)

$-\frac{5}{7}$

d)

-\frac{7}{5}

8.

Solve for x using the same base method:

\frac{1}{4}=16^{\left(2x-5\right)}

a)

$-\frac{11}{4}$

b)

8

c)

$\frac{9}{4}$

d)

6

9.

Evaluate the logarithm:

log₃81

a)

4

b)

$\frac{1}{4}$

c)

-4

d)

$-\frac{1}{4}$

10.

Evaluate the logarithm:
$\log_6\left(\frac{1}{216}\right)$

a)

3

b)

$\frac{1}{3}$

c)

$-\frac{1}{3}$

d)

-3

11.

Solve the logarithmic equation:

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

12.

Solve the logarithmic equation:

log₄(3x-1)=log₄(2x+3)

Remember to check your answer! You can't take the log of 0 or a negative number.

a)

4

b)

3

c)

1

d)

8

13.

Solve the logarithmic equation:

log₂(x²- 6) = log₂(2x+2)

Remember to check your answer! You can't take the log of 0 or a negative number.

a)

4

b)

6

c)

4, 6

d)

No solution

14.

$\log_26+\log_23$

Condense the expression into a single logarithm.

a)

$\log_218$

b)

$\log_22$

c)

$\log_23$

d)

$\log_29$

15.

$\log_216-\log_24$

Condense the expression into a single logarithm. Simplify if possible.

a)

$\log_24^{16}$

b)

$\log_264$

c)

$\log_28$

d)

$\log_24$

16.

$\log_3\left(\frac{4}{5}\right)$

Expand using the quotient property.

a)

$\log_35-\log_34$

b)

$\log_34-\log_35$

c)

$\log_3\left(20\right)$

d)

$\log_34^5$

17.

$3\log_42$

Condense the expression into a single logarithm. Simplify if possible.

a)

$\log_48$

b)

$\log_42$

c)

$\log_43$

d)

$\log_49$

18.

$\log_57^2$

Expand using the power property of logs.

a)

$49\log_51$

b)

$7\log_52$

c)

$\log_549$

d)

$2\log_57$

19.

Solve the equation using properties of logs:

log₂(x + 2) + log₂x = 3

Remember to check your answer! You can't take the log of 0 or a negative number.

a)

-4, 2

b)

2

c)

4, -2

d)

No solution

20.

$3\log_2x=\log_28$

Solve the equation using properties of logs.
Remember to check your answer! You can't take the log of 0 or a negative number.

a)

6

b)

$\frac{8}{3}$

c)

8

d)

2

21.

Solve the exponential equation using logs.

3^x=7

a)

$\ln3^7$

b)

$\ln\left(\frac{7}{3}\right)$

c)

$\frac{\ln7}{\ln3}$

d)

$\frac{\ln3}{\ln7}$

22.

Solve the exponential equation using logs.

5^{\left(2x+3\right)}=15

a)

-0.659

b)

-0.528

c)

-2.159

d)

-0.478

23.

Use the change of base formula to solve the equation.

\log_46

a)

0.774

b)

0.778

c)

1.293

d)

0.602

24.

Log with a base "e" (log_e) is the same thing as...

a)

e

b)

Natural Logarithm (ln)

c)

Common Logarithm (log)

d)

Natural Logarithm base e (ln_e)

25.

Rewrite the exponential equation in logarithmic form.

e^x=15

a)

$\log x=15$

b)

$\ln x=15$

c)

$\log15=x$

d)

$\ln15=x$

26.

Solve for x.

3e^{-2x}+4=10

a)

$\frac{\ln\left(\frac{14}{3}\right)}{3}$

b)

$\frac{\ln2}{-2}$

c)

$\frac{\ln\left(\frac{14}{3}\right)}{-2}$

d)

$\frac{\ln2}{3}$

27.

Solve for x.

4\ln\left(x+2\right)=32

a)

$\ln8$

b)

$\ln6$

c)

$e^{32}-2$

d)

$e^8-2$

28.

What is the domain of log(x)?

a)

(-∞, ∞)

b)

[0, ∞)

c)

(0, ∞)

d)

Pickle

29.

What is the range of log(x)?

a)

(-2, 4)

b)

(-∞, ∞)

c)

(-∞, 0)

d)

Cucumber

30.

Match the graph with its equation

a)

y = log₄ (x)+2

b)

y = log₄ (x + 2) + 1

c)

y = log₄ (x - 1) + 2

d)

y = log₄ (-x + 2)

31.

Match the graph with its equation

a)

y = log₆(-x) + 1

b)

y = log₆(x − 2) + 1

c)

y = log₆(x + 2) - 1

d)

y = log(x-8) + 1

Exponential and Logarithms Test Review

Total questions: 31

Worksheet time: 5hrs 10mins

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