Question

If f(x)=2^x find x if f(x)= 1/4

Answer 1

$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)=2^x~\hspace{7em} \begin{cases} f(x)=\cfrac{1}{4} \end{cases} \qquad \qquad \cfrac{1}{4}=2^x\implies \cfrac{1}{2^2}=2^x \\\\\\ 2^{-2}=2^x\implies \stackrel{\textit{if the bases are the same, the exponents must also be the same}}{-2=x}$