# What are some examples of extraneous solutions to equations?

##### 1 Answer

**Example 1** : Raising to an even power

Solve

Raising both sides to the

This requires,

Factoring gives

So we need

The solution set of the last equation is

**Example 2** Multiplying by zero

If you solve

you'll get

which lead to

.

It looks like the solution set is

Both are solutions to the second and third equations, but

**Example 3** : Combining sums of logarithms.

Solve:

Combine the logs on the left to get

This leads to