Free Printable Test 12 Review: Exponents & Logarithms

1.

What does the b in log_bA=x represent?

a)

Argument

b)

Base

c)

Exponent

d)

Bottom

2.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

3.

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

4.

Rewrite the exponential equation into its logarithmic equation; x⁶=64

a)

log₆x=64

b)

log6=64

c)

log₆64=x

d)

log_x64=6

5.

Solve for x
5^x = 17

a)

x = log₁₇5

b)

x = log 5 + log 17

c)

x = log₅17

d)

x = (log 5)/(log 17)

6.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

7.

Write in exponential form

log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

8.

Solve for x.
3^x = 27

a)

2

b)

4

c)

3

d)

5

9.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

10.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

11.

How do you properly read log₁₀100=2?

a)

log base 10 of 100 is equal to 2

b)

log base of 10 is equal to 2

c)

log 100 of 10 is equal to 2

d)

log of 100

12.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

13.

Is the expression true or false; log_baseArgument=exponent

a)

True

b)

False

14.

Rewrite: $e^x=4$

a)

$\ln x=e$

b)

$\log x=4$

c)

$\log4=x$

d)

$\ln4=x$

15.

Rewrite: $10^{-2}=0.01$

a)

$\ln0.01=-2$

b)

$\log_{0.01}-2=10$

c)

$\log_{-2}0.01=10$

d)

$\log0.01=-2$

16.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

17.

Expand ln xy²z³

a)

6(lnx + lny - lnz)

b)

lnx + 2lny - 3lnz

c)

lnx + (1/2)lny + (1/3)lnz

d)

lnx + 2lny + 3lnz

18.

ln e⁵=

a)

e⁵

b)

ln 5

c)

5

d)

5e

19.

Solve the following equation for x. Round your solution to two decimal places.
ln2x - ln41 = 2

a)

x = 0.36

b)

x = 151.48

c)

x = 41

d)

None of these are solutions

20.

Solve for x:
e^2x = 11

a)

x = (LN 11)/2

b)

x = 2log_e11

c)

x = 2eLOG 11

d)

x = LN (11/2)

21.

Solve for x:
2^{3x + 1} = 32

a)

0

b)

-1

c)

5/3

d)

4/3

22.

Condense the logarithms: $5\log a-25\ \log b$

a)

log (a⁵+ b²⁵)

b)

log (a⁵− b²⁵)

c)

log (ab²⁵)

d)

log (a⁵/b²⁵)

23.

Use your calculator (and change of base) to evaluate the logarithm: $\log_583$

a)

3.091

b)

2.365

c)

2.746

d)

1.804

24.

Use your calculator (and change of base) to evaluate the logarithm: $\log_218$

a)

4.965

b)

3.408

c)

4.17

d)

2.212

25.

Change to logarithmic form.

3^h = w

a)

log_w3 = h

b)

log₃w = h

c)

log_h3 = w

d)

log₃h = w

26.

Condense: log₂6+log₂3=

a)

log₂18

b)

log₂2 = 1

c)

log₂3

d)

log₂9

27.

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

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

28.

Expand log₃(9x²)

a)

3+2log₃x

b)

log₃9+2log₃x

c)

2+2log₃x

d)

log9+2logx

29.

Evaluate the following logarithm by converting to exponential form.
log₃⅓ = x

a)

x = -1

b)

x = 1

c)

x = 3

d)

x = ⅓

30.

Which of the following expressions is equivalent to $6\log\left(x\right)-2\log\left(y\right)?$

a)

$\log\left(x^6+y^2\right)$

b)

$\log\left(\frac{6x}{2y}\right)$

c)

$\log\left(\frac{x^6}{y^2}\right)$

d)

$\log\left(x^6\cdot y^2\right)$

31.

If $\log_4\left(a-2\right)=2$ , then a =

a)

14

b)

10

c)

18

d)

6

32.

Which equation is equivalent to

$\log_4\left(\frac{1}{2}\right)=x$ ?

a)

$4^{\frac{1}{2}}=x$

b)

$\left(\frac{1}{2}\right)^4=x$

c)

$4^x=\frac{1}{2}$

d)

$\left(\frac{1}{2}\right)^x=4$

33.

Which of the following represent exponential growth? Check ALL that apply.

a)

b)

c)

d)

e)

34.

The bacteria count in a heated swimming pool is 1,500 bacteria per cubic centimeter on Monday, and the count doubles each day.

Which function correctly represents the number of bacteria after t days?

a)

P\left(t\right)=\left(2\right)^t+1500

b)

$P\left(t\right)=1500\cdot\left(2\right)^t$

c)

$P\left(t\right)=2\cdot\left(1500\right)^x$

d)

$P\left(t\right)=2^{\left(x-1500\right)}$

35.

Solve for x: $\log_5\left(x+2\right)=\log_5\left(3x+5\right)$

a)

$x=\frac{3}{2}$

b)

$x=-\frac{3}{2}$

c)

$x=\frac{7}{2}$

d)

$x=-\frac{3}{4}$

36.

Solve for x: $9^x=60$

a)

1.748

b)

x = 6.667

c)

x = 0.537

d)

x = 1.863

37.

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^twhere t is the number of years since 1990. What was the population in 1990?

a)

0 people

b)

It doesn't say

c)

I don't know

d)

6191

38.

You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. What is the approximate value of the land in the year 2011?

a)

$344,022

b)

$31,500

c)

$15,000

d)

$28,500

39.

An adult takes 400 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%.
What is the multiplier for this problem?

a)

1.29

b)

.71

c)

.29

d)

1.71

40.

An adult takes 400 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%. How much ibuprofen is left after 6 hours?

a)

51 mg

b)

284 mg

c)

1843 mg

d)

116 mg

41.

You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How long until you have 10mg of caffeine?

a)

19 to 20 hours

b)

10 to 20 hours

c)

15 to 16 hours

d)

5 to 6 hours

42.

A sailboat that costs $5,950 decreases in value by 11% per year. How much will the boat be worth after 6 years?

a)

$5,884.00

b)

$5,178.97

c)

$2,992.96

d)

$2,957.04

43.

Does the following equation show growth or decay?
y=10,000*1.26^x

a)

Growth

b)

Decay

44.

Does the following equation show growth or decay?
y=10,000*(0.76)^x

a)

Growth

b)

Decay

45.

Does the following equation show growth or decay?
y=10,000*(1-.05)^x

a)

Growth

b)

Decay

46.

Does the following equation show growth or decay?
y=10,000*(1+.05)^x

a)

Growth

b)

Decay

47.

In 1985, there were 285 cell phone subscribers in the small town of Centerville. The number of subscribers increased by 75% per year after 1985. How many cell phone subscribers were in Centerville in 1994?

a)

OVERFLOW

b)

1994

c)

1000

d)

43871

48.

Bacteria can multiply at an alarming rate when each bacteria splits into two new cells, thus doubling. If we start with only one bacteria which can double every hour, how many bacteria will we have after half of a day?

a)

1024

b)

2048

c)

8192

d)

4096

49.

The population of Hickory NC, can be modeled by P=6191(1.04)t where t is the number of years since 1995. What was the population in 1995?

a)

6191

b)

1

c)

1995

d)

1.04

50.

Use the change of base formula and your calculator to approximate the log.

a)

A

b)

B

c)

C

d)

D

Test 12 Review: Exponents & Logarithms

Total questions: 50

Worksheet time: 3hrs 9mins

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