What is the inverse function of the natural logarithm of x?
The natural logarithm function ln(x) is the inverse function of the exponential function ex.
When the natural logarithm function is:
f (x) = ln(x), x>0
Then the inverse function of the natural logarithm function is the exponential function:
f -1(x) = ex
So the natural logarithm of the exponent of x is x:
f (f -1(x)) = ln(ex) = x
Or
f -1(f (x)) = eln(x) = x