# How do you solve #9^x=3^(x-2)#?

##### 2 Answers

Nov 11, 2015

#### Explanation:

First of all, we need the rule which states that

Then, we observe that

Applying the forementioned rule, we get

Now, if two powers of three are equal, then the exponents must be equal. In fact, it's not possible to give two different exponents to three and obtain the same result. This means that, in technical terms, the exponential is an injective function. So, if

which we can easily solve: subtractin

Nov 11, 2015

I found

#### Explanation:

You could write

to be equal the exponents must be equal: