#### 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.