What is the inverse of #f(x) = 3log(x-1)#?

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Answer 1 · 2018-05-20T16:41:32

#y=log^(-1)(x/3)+1#

Set #y=3log(x-1)#

Divide both sides by 3

#y/3=log(x-1)#

Using older terminology: tale the antilogarithm of both sides (log inverse).

#log^(-1)(y/3)=x-1#

#x=log^(-1)(y/3)+1#

Wherever there was an #x# write #y# and wherever there was a #y# write #x# giving:

#y=log^(-1)(x/3)+1#