## Precalculus (10th Edition)

$2^x=10$.
We know that $\frac{1}{1000}=\frac{1}{10^3}=10^{-3}$ and that $2^{-3x}=(2^x)^{-3}.$ Hence $2^{-3x}=\frac{1}{1000}\\(2^x)^{-3}=10^{-3}$. We know that $a^b=c^b\longrightarrow a=c$ if $b\ne1$. Thus $2^x=10$.