What is the inverse of y=log(x-3)? ?

Nov 1, 2015

$y = {10}^{x} + 3$

Explanation:

The inverse of a logarithmic function $y = {\log}_{a} x$ is the exponential function $y = {a}^{x}$.

$\left[1\right] \text{ } y = \log \left(x - 3\right)$

First we must convert this to exponential form.

$\left[2\right] \text{ } \Leftrightarrow {10}^{y} = x - 3$

Isolate $x$ by adding $3$ to both sides.

$\left[3\right] \text{ } {10}^{y} + 3 = x - 3 + 3$

$\left[4\right] \text{ } x = {10}^{y} + 3$

Finally, switch the positions of $x$ and $y$ to get the inverse function.

$\left[5\right] \text{ } \textcolor{b l u e}{y = {10}^{x} + 3}$