Question

What is the correct inverse function for f(x) = ln5x?

Answer 1

f^-1 (x) = e^x / 5

Replace y for x and x for y then solve for y

Y= ln5x
X=ln5y
X/ln5=y
e^x/5=y

Answer 2

Inverse of f(x) = ln5x ,
`f^(-1)(x)=(e^x)/(5)`

Explanation:

We have f(x) = ln 5x

y = ln x

For finding inverse replace x by y and y by x

x = ln 5y

`e^x=e^(ln5y)\\\\5y=e^x\\\\y=(e^x)/(5)`

So, inverse of f(x) = ln5x ,
`f^(-1)(x)=(e^x)/(5)`