How do you find the inverse of #y=4^x#?

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Answer 1 · 2018-04-17T21:28:43

#y=lnx/ln4#

Switch the places of #x, y# and subsequently solve for #y:#

#y=4^x#

#x=4^y#

#ln(4^y)=lnx#

We need to get an explicit solution, IE, isolate #y.# Recalling that #ln(a^b)=blna#:

#yln(4)=lnx#

#y=lnx/ln4#