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#