Free Printable Exponential/Log Review

1.

What is the transformation?

a)

Vertical Translation up 2 and Horizontal translation right 1

b)

Vertical Translation down 2 and Horizontal Translation left 1

c)

Horizontal Translation left 2 and Vertical Translation up 1

d)

Horizontal Translation right 2 and Vertical Translation down 1

2.

Solve for p:
4^p+2 = 64

a)

p = -16/9

b)

p = 1

c)

p = 8

d)

p = 7/6

3.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

4.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

5.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

6.

Solve for x:

log₂(x + 5) = 3

a)

3

b)

4

c)

5

d)

6

7.

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)

$\log x-\log6y$

8.

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

a)

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

b)

$12\log_{ }\ xyz$

c)

$\log_{ }\ 3x4yz$

d)

logx³y³z³

9.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

10.

Rewrite the following exponent as a logarithm $e^4=x$ .

a)

$e^x=4$

b)

$\ln e=4$

c)

$\ln x=4$

d)

$\log4=e$

11.

Rewrite the logarithmic equation in exponential form $\ln3=x$ .

a)

$x=0$

b)

$e^3=x$

c)

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

d)

$e^x=3$

12.

Simplify e^ln(x)

a)

0

b)

1

c)

x

d)

8

13.

Expand $\ln\ x^5y^2$

a)

5lnx + ln2y

b)

lnx5y2

c)

5lnx + 2lny

d)

5lnx - 2lny

14.

Solve $3e^x=63$
Round your answer to the nearest hundredth

a)

2.74

b)

3.04

c)

2.88

d)

2.96

15.

An antibiotic is introduced into a colony of 12,000 bacteria during a laboratory experiment. The colony is decreasing by 14.9% per minute. Which function can be used to model the number of bacteria in the colony after x minutes?

a)

f(x) = 12000(1 + 14.9)^x

b)

f(x) = 12000(1 - 14.9)^x

c)

f(x) = 12000(1 + 0.149)^x

d)

f(x) = 12000(1 - 0.149)^x

16.

Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?

a)

$176,783.29

b)

$424,527.63

c)

$57,357.75

d)

$532,041,076.80

17.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

18.

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

19.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

20.

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

21.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

22.

The base of common log is 10. So log 100 = ?

a)

1

b)

2

c)

10

d)

50

23.

Solve $\log_2\left(x+8\right)=\log_264$

a)

x=16

b)

x=24

c)

x=56

d)

x=40

24.

Solve $\log_6x+\log_69=\log_654$

a)

x=6

b)

x=45

c)

x=7

d)

x=36

25.

log₆(2x + 3) = 3

a)

x = 106.5

b)

x = 100

c)

x = 16

d)

x = 50

26.

Expand the following: $\log_7\left(4x\right)$

a)

$\log_7\left(4\right)+\log_7\left(x\right)$

b)

$\log_7\left(4\right)-\log_7\left(x\right)$

c)

$\log_7\left(x^4\right)$

d)

$4\log_7\left(x\right)$

27.

Simplify the following: $\log_324-\log_36$

a)

$\log_318$

b)

$\log_3144$

c)

$\log_34$

d)

$\log12$

e)

$18\log3$

28.

Write the equation in exponential form.
$\ln87=x+4$

a)

$e^{\left(x+4\right)}=87$

b)

$e^{87}=x+4$

29.

Expand the logarithmic expression.

$\ln\left(\frac{m^5}{n^2}\right)^3$

a)

$\ln\left(\frac{m^{15}}{n^6}\right)$

b)

$15\cdot\ln m-6\cdot\ln n$

c)

$15\cdot\ln m+6\cdot\ln n$

d)

$\ln m^{15}-\ln n^6$

30.

Condense the expression as a single logarithm.

$\ln4+\ln3x$

a)

$\ln7x$

b)

$\ln\left(3x\right)^4$

c)

$\ln12x$

31.

Condense the expression as a single logarithm.

$\frac{1}{2}\cdot\ln256-3\cdot\ln2$

a)

$\ln128$

b)

$\ln8$

c)

$\ln32$

d)

$\ln2$

32.

Kimi invests $4,000 at 3% interest compounded continuously. How much money will she have in 4 years?

(a)

33.

Principal: $5000
Interest Rate: 3.75%
Time: 25 years
Compounded Monthly
State the future account balance.

a)

$12712.31

b)

$12,749.30

c)

$12,657.59

d)

$12550.84

34.

Jack invest $600 earning 5% interest rate. How much will he have after 5 years?

a)

$630

b)

$729.30

c)

$765.77

d)

$4556.25

35.

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

a)

14327

b)

4309

c)

839

d)

7680

Exponential/Log Review

Total questions: 35

Worksheet time: 2hrs 15mins

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