Answer
$x=2,4$
Work Step by Step
Re-write the given equation as: $(5^3)^{2x}=5^{x^2+8}$
or, $5^{6x}=5^{x^2+8}$
Use the rule power rule: $a^p=a^q$.
We can see that the base $a=5$ is the same on both sides of the equation.
So, the exponents will also be equal.
This implies that $p=q$
Therefore, $x^2+8=6x \\ x^2-6x+8=0 \\ (x-4)(x-2)=0$
By the zero-product property, we have: $x=2,4$
