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