Question

How do you solve this equation ​

Answer 1

$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ e^{x-6}=\left( \cfrac{1}{e^4} \right)^{x+2}\implies e^{x-6}=\left( e^{-4} \right)^{x+2}\implies \stackrel{\textit{same bases, same exponents}}{e^{x-6}=e^{-4x-8}} \\\\\\ x-6=-4x-8\implies 5x=-2\implies x=-\cfrac{2}{5}$