# How to evaluate logarithms

This lesson will show how to evaluate logarithms with three good examples. Study them carefully.

Example #1:

Evaluate log8 16

Write an equation in logarithmic form

log8 16 = x

Convert to exponential form

16 = 8x

Write each side using base 2.

24 = (23)x

24 = 23x

Since the base or 2 is the same,   24 = 23x   if 4 is equal to 3x

If 4 = 3x, then  x = 4/3

Therefore, log8 16 = x = 4/3

Example #2:

Evaluate log10 1000

Write an equation in logarithmic form

log10 1000 = x

Convert to exponential form

1000 = 10x

Write each side using base 10.

103 = (10)x

Since the base or 10 is the same,   103 = 10x   if 3 is equal to x

Therefore, log10 1000 = x = 3

Example #3:

Evaluate log64  1/16

Write an equation in logarithmic form

log64 1/16 = x

Convert to exponential form

1/16 = 64x

Write each side using base 4.

1/42 = (43)x

4-2 = 43x

Since the base or 4 is the same,   4-2 = 43x   if -2 is equal to 3x

If -2 = 3x, then  x = -2/3

Therefore, log64  1/16 = x = -2/3

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