How do you find the inverse of #e^(2x )# and is it a function?

Question

33416 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-11T22:44:33

#x=ln(y)/2#

You have #y=e^(2x)#.
To do the inverse you want to have somehing in the form

#x=f(y)#

To obtain this we start applying the inverse function og the exponential on both side of our firse equation. Such inverse is the #ln#

#y=e^(2x)#

#ln(y)=ln(e^(2x))#

#ln(y)=2x#

and now, dividing by two we have

#x=ln(y)/2#

that is the desired inverse function.