what is the inverse of ln3x?

Answer 1

y= ln(3x)
e^y = 3x
x=(e^y)/3
so the inverse function is:
f^{-1}(y) = (e^y)/3 .

Answer 2

Set the equation equal to y:

y = ln(3x)

Then to find the inverse, swap all x's with y's and vice versa:

x = ln(3y)

Then solve for y, first by raising both sides to the power of e. (e and ln are inverse functions; e^(ln x) = x)

e^x = 3y

Divide by 3:

e^x/3 = y

And that's your answer. The inverse of ln(3x) is 1/3e^(3x).