# How do extraneous solutions arise?

##### 1 Answer

In general, extraneous solutions arise when we perform non-invertible operations on both sides of an equation. (That is, they sometimes arise, but not always.)

**Non-invertible operations** include: raising to an even power (odd powers are invertible), multiplying by zero, and combining sums and differences of logarithms.

**Example** :

The equations:

Square both sides of

Square both sides of