Inverse of e to the power 2x?

1 Answer
Apr 20, 2018

y=lnx/2

Explanation:

So, we have

y=e^(2x) and want to find its inverse. As a result, we'll switch the places of x, y and subsequently solve for y:

x=e^(2y)

Applying the logarithm to both sides:

ln(e^(2y))=lnx

Recalling that ln(a^b)=blna,

2ylne=lnx

ln(e)=1, so

2y=lnx

y=lnx/2