How can your rewrite a logarithm expression?
Before you try to understand the formula for how to rewrite a logarithm equation as exponential equation, you should be comfortable solving exponential equations
As the examples below will show you, a logarithmic expression like $$ log_2 256 $$ is simply a different way of writing an exponent!
Examples
Example 1
Evaluate: $$ log_5 25 $$
Example 2
Evaluate: $$ log_4 64 $$
Example 3
Evaluate: $$ log_4 16 $$
Example 4
Evaluate: $$ log_4 216 $$
Practice Problems
Rewrite as equation
$$ log_4 8 = x $$
Bottom, base. End exponent:
$$ 4^x = 8 $$
$$ 4^x = 8 \\ 4^{\frac{3}{2}} =8 \\ x =\frac{3}{2} $$
Rewrite as equation
$$ log_8 16= x $$
Bottom, base. End exponent:
$$ 8^x = 16 $$
$$ 8^x = 16 \\ 8^{\frac{4}{3}} = 16 \\ x =\frac{4}{3} $$
Rewrite as equation
$$ log_{25} 125= x $$
Bottom, base. End exponent:
$$ 25^x = 125 $$
$$ 25^x = 125 \\ 25^{\frac{3}{2}} = 125 \\ x =\frac{3}{2} $$
Rewrite as equation
$$ log_{145} 1= x $$
Bottom, base. End exponent:
$$ 145^x = 1 $$
$$ 145^x = 1 \\ x =0 $$
Remember any number raised to an exponent of 0, zero, is 1.
