Question

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

Answer 1

`y=10^x+3`

Explanation:

The inverse of a logarithmic function `y=log_ax` is the exponential function `y=a^x`.

`[1]" "y=log(x-3)`

First we must convert this to exponential form.

`[2]" "hArr10^y=x-3`

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

`[3]" "10^y+3=x-3+3`

`[4]" "x=10^y+3`

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

`[5]" "color(blue)(y=10^x+3)`