Q:

Given that $9^{2x} = 27^{x^2 - 5}$. Find the possible values of $x$.

Given that $9^{2x} = 27^{x^2 - 5}$. Find the possible values of $x$.
I don't know how to approach this question.

A:

Hints:

$9=3^2$
$27=3^3$
$(a^b)^c = a^{bc}$
$a^x = a^y$ if and only if $x=y$.

A:

Using that $$3^{4x}=3^{3x^2-15}$$ we get the equation $$4x=3x^2-15$$

