How do you find the inverse of $y=ln(x+2)$ ?

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Answer 1 · 2015-12-15T01:37:24

$y = e^x-2$

The easiest way to find the inverse of a function is to swap $x$ and $y$ and solve for $y$ :

$y = ln(x+2) -> x = ln(y+2)$

We then raise $e$ to the power of both sides to remove the natural logarithm:

$x = ln(y+2) -> e^x = y+2$

And subtract $2$ to isolate $y$ :

$e^x = y+2 -> e^x-2 = y$

Making our final answer $y = e^x-2$

How do you find the inverse of y=ln(x+2)y=ln(x+2)?