Question

simplify e^(3x)/ (e^(2x))^2 * ln (e^x).

Answer 1

\[\frac{e^{3x}}{(e^{2x})^2} *\ln e^x\]
\[\frac{e^{3x}}{e^{4x}}*\ln e^x\]
\[\frac1{e^x}*\ln e^x\]
\[e^{-x}\ln e^x\]
\[\large \color{blue}{iff~~x>0}\]
\[e^{-x}\ln e^x = xe^{-x}\]