# How do you find the inverse of y = log (x/2)?

Dec 16, 2015

$\textcolor{w h i t e}{\times} {f}^{-} 1 \left(x\right) = 2 \times {10}^{x}$

#### Explanation:

$\textcolor{w h i t e}{\times} y = \log \left(\frac{x}{2}\right)$

$\implies \frac{x}{2} = {10}^{y} \textcolor{w h i t e}{\times \times \times \times \times \times}$ (logarithm definition)
$\implies \textcolor{red}{2 \times} \frac{x}{2} = \textcolor{red}{2 \times} {10}^{y}$
$\implies x = 2 \times {10}^{y}$

${f}^{-} 1 \left(x\right) = 2 \times {10}^{x}$