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

Step 1

Rewrite as equation

$$log_4 8 = x$$

Step 2

Bottom, base. End exponent:

$$4^x = 8$$

Step 3

$$4^x = 8 \\ 4^{\frac{3}{2}} =8 \\ x =\frac{3}{2}$$

Step 1

Rewrite as equation

$$log_8 16= x$$

Step 2

Bottom, base. End exponent:

$$8^x = 16$$

Step 3

$$8^x = 16 \\ 8^{\frac{4}{3}} = 16 \\ x =\frac{4}{3}$$

Step 1

Rewrite as equation

$$log_{25} 125= x$$

Step 2

Bottom, base. End exponent:

$$25^x = 125$$

Step 3

$$25^x = 125 \\ 25^{\frac{3}{2}} = 125 \\ x =\frac{3}{2}$$

Step 1

Rewrite as equation

$$log_{145} 1= x$$

Step 2

Bottom, base. End exponent:

$$145^x = 1$$

Step 3

$$145^x = 1 \\ x =0$$

Remember any number raised to an exponent of 0, zero, is 1.

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