Answer
$x=7,-1$
Work Step by Step
Re-write the given equation as: $(3^3)^{2x}=3^{x^2-7}$
or, $3^{6x}=3^{x^2-7}$
Use the rule power rule: $a^p=a^q$.
We can see that the base $a=2$ is the same on both sides of the equation.
So, the exponents will also be equal.
This implies that $p=q$
Therefore, $x^2-7=6x \\ x^2-6x-7=0 \\ (x-7)(x+1)=0$
By the zero-product property, we have: $x=7,-1$
