How do you find the inverse of #f(x) =3(2^x)#?

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Answer 1 · 2015-11-27T17:06:16

#y=(ln(x)-ln(3))/ln(2)#

Write as# color(white)(..) y=3(2^x)#

Take logs

#ln(y)=ln(3)+ln(2^x)#

But # color(white)(..)ln(2^x)=xln(2)# giving:

#ln(y)=ln(3)+xln(2)#

#x=(ln(y)-ln(3))/ln(2)#

Swap #x " and " y# around giving:

#y=(ln(x)-ln(3))/ln(2)#