# How do you solve 3^(x-2)=81?

Oct 1, 2016

$x = 6$

#### Explanation:

It really is an advantage to learn the powers up to 1,000.

Exponential equations fall into two categories..

Those which can be done mentally or with very easy calculations.
Those which require logs,

This one falls into the former where you need to make either the bases the same or the indices the same

Note: ${3}^{4} = 81$

So, 81 can be written as a power of 3.

${3}^{x - 2} = {3}^{4} \text{ } \leftarrow$ bases are equal, so the indices are equal.

$x - 2 = 4$

$x = 6$