[tex]\bf \textit{Logarithm Cancellation Rules}\\\\
\boxed{log_a a^x\implies x}\qquad \qquad a^{log_ax}=x\\\\
-------------------------------\\\\
%e2x = 100
e^{2x}=100\implies log_e(e^{2x})=log_e(100)\implies 2x\cdot log_e(e)=log_e(100)
\\\\\\
x=\cfrac{log_e(100)}{2log_e(e)}\implies \boxed{x=\cfrac{ln(100)}{2ln(e)}}\implies x=\cfrac{log_e(100)}{2log_e(e)}
\\\\\\
x=\cfrac{log_e(10^2)}{2log_e(e)}\implies x=\cfrac{2log_e(10)}{2log_e(e)}
\\\\\\
x=\cfrac{2log_e(10)}{2(1)}\implies x=ln(10)[/tex]
