Free Printable 2.3 Common Logarithm

1.

What is the understood base if no base is written in a logarithm?
$\log\ 100$ for example is log base __________ of 100.

a)

2

b)

1

c)

100

d)

10

2.

I have to find the approximate solution to the problem $\log_8\ 13.$ Which of the following would give me the result?

a)

$\frac{\log13}{\log\ 8}$

b)

$\frac{\log8}{\log13}$

c)

$\log13-\log8$

d)

$\log8+\log13$

3.

Use your calculator to solve. Round to four decimal places.

$\log_7\ 5$

a)

0.8271

b)

1.2091

c)

0.1461

d)

1.5441

4.

Which of the following are equivalent to x in the equation $5^x=25?$ Select all that apply.

a)

$2$

b)

$\log_{25}\ 5$

c)

$\log_5\ 25$

d)

$\frac{\log25}{\log5}$

e)

$\frac{\log5}{\log25}$

5.

Use your calculator and evaluate $\log_2\ 9.$ Round your answer to four decimal places.

(a)

6.

Solve. Round to four decimal places.
$9^x=45$

(a)

7.

Solve. Round to four decimal places.

$8.2^{n-3^{ }}=42.5$

n=

(a)

8.

The expression $\log\left(x-5\right)\$ is undefined for all values of x such that...

a)

$x\le5$

b)

$x>5$

c)

$x\le0$

d)

$x>1$

9.

If $2^4=3^x,$ then what is the value of x?

a)

0.63

b)

2.34

c)

2.52

d)

4

10.

Solve. Round your answer to four decimal places.
$5^x=52$
$x=$ (a)

11.

7^y = 15

a)

2.8970

b)

1.3917

c)

1.8956

d)

5.2342

12.

5^3b = 106

a)

2.9605

b)

1.9659

c)

0.9659

d)

2.9638

13.

2.4^{x + 4} = 30

a)

0.2896

b)

-0.2543

c)

0.1152

d)

-0.1150

14.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

15.

Solve the log by using change of base )

log₄32

a)

8

b)

5/2

c)

2/5

d)

3/2

16.

Use the change of base rule to rewrite this problem:

log₃64

a)

log(64)/log(3)

b)

log(3)/log(64)

17.

What is the simplified expression of log 10?

a)

10

b)

0

c)

1

d)

-1

18.

What is the value of x in the logarithmic equation log (3x-2) = log 2?

a)

4/3

b)

3/4

c)

2

d)

2/3

2.3 Common Logarithm

Total questions: 18

Worksheet time: 30mins

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