Answer
$x=\frac{3}{2}$
Work Step by Step
We are given the equation $100^{x}=1000$. First, we must write both sides using the same base.
$((10)^{2})^{x}=10^{2x}=10^{3}$
Next, we must take the natural log of both sides.
$ln(10^{2x})=ln(10^{3})$
$2xln(10)=3ln(10)$
Divide both sides by $ln(10)$.
$2x=3$
Divide both sides by 2.
$x=\frac{3}{2}$