Question

How do you find the inverse of \[y = \ln x\]?

Answer 1

Hint:
In the given question, we have been given a function. This function is the logarithmic function with a base of “e” (The Euler’s Number) with a variable argument. We have to find the inverse of this logarithmic function. To do that, we swap the variables and then solve for the argument variable (the swapped one). That gives us the inverse of the original function.

Formula Used:
We are going to use the formula of log inverse, which is:
\[{e^{\ln A}} = A\]

Complete step by step answer:
The given function whose inverse is to be found is
\[y = \ln x\]
We swap the variables,
\[x = \ln y\]
Now, we solve for \[y\]
To do that, let us raise both the sides to the power of \[e\], and we get:
\[{e^x} = {e^{\ln y}}\]
Using the log inverse formula, we get,
\[y = {e^x}\]

Hence, \[{y^{ - 1}} = {e^x}\]

Note:
In the given question we had to find the inverse of the natural log function. To do that, we take the variable equal to the log function, swap the variables and then solve for the swapped variables. That simply gives us the answer.