Free Printable Logs & Exponentials

1.

Rewrite as an exponential: log₂8 = 3

a)

3² = 8

b)

2³ = 8

c)

2⁸ = 3

d)

8³ = 2

2.

Rewrite as an exponential: $\log_7\left(\frac{1}{49}\right)=-2$

a)

$7^{\frac{1}{49}}=-2$

b)

$\left(\frac{1}{49}\right)^{-2}=7$

c)

$7^{-2}=\frac{1}{49}$

d)

$\left(-2\right)^7=\frac{1}{49}$

3.

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)

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

4.

Rewrite as a log: y = 7^x

a)

log₇(x) = y

b)

log_y(7) = x

c)

log_x(y) = 7

d)

log₇(y) = x

5.

Rewrite as a log: x = 11^y

a)

log₁₁(y) = x

b)

log_y(11) = x

c)

log₁₁(x) = y

d)

log_x(y) = 11

6.

Rewrite as a log: 7⁰ = 1

a)

log₇(1) = 0

b)

log₀(7) = 1

c)

log₇(0) = 1

d)

log₁(0) = 7

7.

What is the base for the following log:

y = log (x)

a)

1

b)

0

c)

10

d)

2

8.

Find x: log₂(32) = x

a)

x = 5

b)

x = 16

c)

x = 4

d)

x = 6

9.

Find x: log₅(x) = 4

a)

x = 20

b)

x = 25

c)

x = 625

d)

x = 125

10.

Find x: log_x(25) = 2

a)

x = 1

b)

x = 12.5

c)

No Solution

d)

x = 5

11.

Find x: $\log_7\left(\frac{1}{7}\right)=x$

a)

x = -1

b)

x = 1

c)

x = 0

d)

No Solution

12.

Find x: log₅(x) = 0

a)

No Solution

b)

x = 0

c)

x = 5

d)

x = 1

13.

Find x: $\log_x\left(\frac{1}{8}\right)=-3$

a)

x = 2

b)

x = -2

c)

x = 2.67

d)

No Solution

14.

Find the exponential equation that represents the table.

a)

y = 2(3)^x

b)

y = 3 + (3)^x

c)

y = 3(2)^x

d)

y = 6(2)^x

15.

Find the equation of the exponential function that passes through the points (2, 1) and (4, 0.25).

a)

y = 0.25(2)^x

b)

y = 4(0.5)^x

c)

y = 1(0.5)^x

d)

y = 0.5(2)^x

16.

Find the equation of the exponential function that passes through the points (1, 12) and (4, 768).

a)

y = 12(4)^x

b)

y = 1.5(8)^x

c)

y = 3(4)^x

d)

y = 1.33(9)^x

17.

A chemical substance has a half-life of 3 days. If you start with 90 grams of the substance, how much will be left after 13 days? Write an equation to help you find your answer.

a)

about 4.487 grams

b)

about 0.011 grams

c)

about 0.9924 grams

d)

about 4.221 grams

Logs & Exponentials

Total questions: 17

Worksheet time: 1hrs 25mins

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