Answer
$x=\frac{3}{5}$
Work Step by Step
We are given the exponential equation $32^{x}=8$.
We can express each side using a common base and then solve for $x$.
$32^{x}=(2^{5})^{x}=2^{5x}$
$8=2^{3}$
$2^{5x}=2^{3}$
Take the natural log of both sides.
$ln(2^{5x})=ln(2^{3})$
$5xln(2)=3ln(2)$
Divide both sides by $ln(2)$.
$5x=3$
Divide both sides by 5.
$x=\frac{3}{5}$
