Does ${f(x)=\ln(e^{x^2})}$ reduce to ${x^2\ln(e)}$ or ${2x\ln(e)}$? I'm confused with the expression  ${f(x) = \ln(e^{x^2})}$.I know the rule  ${\log_a(x^p) = p\log_a(x)}$. So does the given expression reduce to ${x^2\ln(e)}$ or ${2x\ln(e)}$?

Here you have $\ln(e^p)$ with $p = x^2$, so the correct reduction is $(x^2)\ln(e) = x^2$.
