Answer
$x=-1$
Work Step by Step
We are given the equation $10^{x}=.1=\frac{1}{10}$. First, we must write both sides using the same base.
$10^{x}=10^{-1}=\frac{1}{10}$
Next, we must take the natural log of both sides.
$ln(10^{x})=ln(10^{-1})$
$xln(10)=-1ln(10)$
Divide both sides by $ln(10)$.
$x=-1$
