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Example 1

Solve: log_{x} 100 = 2.

Rewrite in exponential form.

Take the square root of each side.

Simplify.

x^{2} =

x =

100

Â± 10

Since x is the base, it must be positive. Therefore, -10 is not a solution. The solution is x = +10.

So, log_{10}100 = 2. The solution checks since 10^{2} = 100. You may also check the solution on a calculator.

Example 2

Solve:

Rewrite using a radical.

Square both sides.

x

= 8

= 64

So,

Note:

The solution of is x = 64.

Here is a check.

Example 3

Rewrite x^{-2} as .

x = Â±

x = Â± 4

So, We leave the check to you.