# How do you solve for x in #18^(x-2) = 13^(-2x)#?

##### 1 Answer

Sep 28, 2015

#### Explanation:

Since 13 is a prime and 18 is a compound number without 13 as a prime factor you'll never be able to equate bases, therefore, we'll need to apply logs. I'm using the natural base due to preference you can use whatever base you want - that being said, I'd recommend using natural or decimal.

Isolating x

You could break down some of these logs further but since the problem gave 18 and 13 as numbers, I'd leave the answer in terms of their logs.