Answer
$(-\infty,\infty)$
Work Step by Step
We have to solve the exponential equaation:
$5^{8(x-1)}=625^{2x-2}$
Rewriting $625=5^{4}$, we have
$5^{8x-8}=(5^{4})^{2x-2}$
$\implies 5^{8x-8}=5^{8x-8}$
Equating the exponents, we get
$8x-8=8x-8$
Or $0=0$ which is always true.
So the above equation has infinitely many solutions.
