Practice Logarithm in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The logarithm log⁡b(x) answers: "to what power must b be raised to produce x?" It is the inverse function of f(x)=bx.

The exponent that produces a number. log⁡2(8)=3 because 23=8.

Showing a random 20 of 50 problems.

Example 1

medium
Use log⁡b(xy)=log⁡bx+log⁡by to expand log⁡2(8⋅16).

Example 2

medium
Evaluate log⁡100.001.

Example 3

easy
Evaluate log⁡327.

Example 4

medium
Simplify log⁡5100−log⁡54.

Example 5

challenge
Solve log⁡2x+log⁡4x=3.

Example 6

medium
Solve 2x=50 for x to two decimal places.

Example 7

easy
Evaluate ln⁡e.

Example 8

hard
Solve log⁡2(x)+log⁡2(x−6)=4.

Example 9

easy
What is the domain of log⁡2x?

Example 10

easy
Evaluate log⁡28.

Example 11

easy
Rewrite 53=125 as a logarithm.

Example 12

easy
Evaluate log⁡416.

Example 13

hard
What is the domain of f(x)=log⁡2(x−3)?

Example 14

easy
Rewrite 24=16 as a logarithm.

Example 15

easy
What is log⁡b1 for any base b?

Example 16

hard
Solve log⁡(x+1)+log⁡(x−1)=log⁡8 where log⁡=log⁡10.

Example 17

medium
Solve log⁡3x=4.

Example 18

easy
Evaluate log⁡51.

Example 19

easy
Evaluate log⁡218.

Example 20

challenge
If log⁡b2=0.3 and log⁡b3=0.5, find log⁡b12.
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