## Functions Modeling Change: A Preparation for Calculus, 5th Edition

$4x$ ($x \gt 0$)
Use the fact that $10^2=100$ and $(a^m)^n=a^{mn}$ to rewrite the expression as $$\log(10^2)^{2x}=\log 10^{4x}$$ Since $\log 10^a=a$, the expression becomes $4x$. (Note that $x$ must be positive for the log to output a real value.)