g(x)=2^-x

OR

$$\begin{array}{rll}
g(x)&=&2^{-x}\\
log_2[g(x)]&=&log_2\;2^{-x}\\
x&=&-log_2[g(x)]




\end{array}$$

g(x)=2^-x find x

$$\begin{array}{rcl}
g(x) &=& 2^{-x} \quad | \quad \ln() \\\\
\ln{(g(x))} &=& -x\ln{(2)} \\\\
\boxed{x = - \frac{ \ln{(g(x))} } {\ln{(2)} }}
\end{array}$$