Answer
$x=4$
Work Step by Step
The given equation contains radicals:
$(\sqrt[5] {3})^{5x-10}=(\sqrt[8] {3})^{4x}$
Rewriting $\sqrt[5] 3$ as $3^{\frac{1}{5}}$ and $\sqrt[8] 3$ as $3^{\frac{1}{8}}$, we have
$(3^{\frac{1}{5}})^{5x-10}=(3^{\frac{1}{8}})^{4x}$
$\implies 3^{x-2}=3^{\frac{x}{2}}$
Equating the exponents, we obtain
$x-2=\frac{x}{2}$
$\implies 2(x-2)=x$
$2x-4=x$
$2x-x=4$
$x=4$
