[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad a^{log_a x}=x \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \ln\left( e^{-6x} \right)\implies \log_e\left( e^{-6x} \right)\implies -6x \\\\\\ e^{4\ln(x)}\implies e^{\ln(x)4}\implies e^{\log_e(x)4}\implies \left[ e^{\log_e(x)} \right]^4\implies [x]^4\implies x^4 \\\\\\ e^{\ln(4x)+2}\implies e^{\ln(x)}\cdot e^2\implies e^{\log_e(x)}\cdot e^2\implies xe^2[/tex]
