Answer
Solution set = $\displaystyle \{ \frac{1}{2} \}$
Work Step by Step
$5^{2x}\cdot 5^{4x}=125$
LHS: $ a^{n}\cdot a^{m}=a^{n+m}$
RHS: $125=5^{3}$
$5^{2x+4x}=5^{3}$
$ 5^{6x}=5^{3}\qquad $ ... exponential functions are one to one.
$6x=3$
$ x=\displaystyle \frac{1}{2}$
Solution set = $\displaystyle \{ \frac{1}{2} \}$
