Free Printable Log and Exp Test Review

1.

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

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

2.

Given log₂(x + 5) = 3 the first step to solve this equation is

a)

2³ = x + 5

b)

3² = x + 5

c)

2^x = 3 - 5

d)

none of these

3.

Condense:

log4 − logx − log5+log3

a)

\log\left(\frac{20}{3x}\right)

b)

$\log\left(\frac{12x}{5}\right)$

c)

$\log\left(\frac{12}{5x}\right)$

d)

$\log\left(\frac{5x}{12}\right)$

4.

Solve

2³ⁿ = 4 by re-writing as 2³ⁿ = 2² then n =

a)

2

b)

3

c)

2/3

d)

4

5.

Simplify (evaluate): $-2\log_4\left(4\right)^5$

a)

\frac{1}{10}

b)

-40

c)

-32

d)

-10

6.

$4\log_3\sqrt{3}$

evaluate:

a)

-2

b)

2

c)

16

d)

64

7.

The first step to solve 8 = 2^5x+7 is

a)

8 = 5x + 7

b)

2³ = 5x + 7

c)

2³ = 2^{5x + 7}

d)

none of these

8.

Solve 8 = 2^5x+7

a)

x = ⅘

b)

x = ¼

c)

x = -⅘

d)

x = -¼

9.

Which equation leads to the solution of

log (x) + log (x) = log (25) is

a)

2x = 25

b)

x² = 25

c)

x + x = 25

d)

none of these

10.

log (x) + log (x) = log (25) and x² = 25 have the same solutions.

a)

True, both 5 and -5

b)

False, -5 does not work for the log equation

11.

Which equation leads to the solution of

log₂(x + 2) + log₂x = 3

a)

x² + 2x = 3

b)

2x + 2 = 3

c)

2³ = x² + 2x

d)

none of these

12.

log₂(x + 2) + log₂x = 3 changes to

x² + 2x − 8 = 0, so the the correct solution to the first equation is

a)

-4, 2

b)

-2, 4

c)

2 ; -4 is extraneous

d)

1 ; -3 is extraneous

13.

Which equation leads to the solution of

log (x −1) − log (x − 2) = log 5 ?

a)

(x−1)(x−2) = 5

b)

(x−1) − (x−2) = 5

c)

$\frac{x-1}{x-2}\ =\ 5$

d)

$\frac{x-2}{x-1}=5$

14.

Choose an equation that leads to the solution of the one shown.

a)

log₃(x − 9) = 24

b)

3^-4 = x − 3

c)

3⁴ = x − 3

d)

none of these

15.

What equation matches the graph?

a)

f(x) = 3^x

b)

f(x) = (⅓)^x

c)

f(x) = log₃(x)

16.

Choose the equation of the graph shown by evaluating each equation at x = 0.

a)

b)

c)

d)

17.

Which equation matches the pink graph?

a)

$y=2^{\left(x+2\right)}$

b)

$y=2^x+2$

c)

$y=2^{\left(x-2\right)}$

d)

$y=2^x-2$

18.

Which equation matches the green graph?

a)

$y=2^{\left(x+2\right)}$

b)

$y=2^x+2$

c)

$y=2^{\left(x-2\right)}$

d)

$y=2^x-2$

19.

Which equation matches the red graph?

a)

y = -3^x

b)

y = 3^-x

c)

y= -3^-x

d)

y = 3 - x

20.

$\log_2\ \left(\frac{1}{8}\right)\ +\log_24$

Evaluate

a)

-3

b)

-2

c)

-1

d)

1

Log and Exp Test Review

Total questions: 20

Worksheet time: 2hrs 37mins

Similar Resources on Wayground