Inverse of e to the power 2x?

Question

3126 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-20T01:35:19

#y=lnx/2#

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#