# Is the logarithmic function inverse of an exponential function?

**Solution:**

We will use the concept of inverse function to find the inverse of the exponential function.

Let us see how we will use the concept of inverse function to find the inverse of the exponential function.

Let us consider an exponential function y = e^{ax + b}.

In order to find the inverse of the function we have to find the value of x in the above function and that will be the inverse of the function y.

Taking log to both sides we get,

log (y) = ax + b

ax = log (y) - b

x = [ log (y) - b ] / a

Hence , inverse of function y is y^{'} = [ log (x) - b ] / a

Hence, we can conclude that the inverse of exponential function is logarithmic function.

## Is the logarithmic function inverse of an exponential function?

**Summary:**

The inverse of an exponential function is a logarithmic function. If y = e^{ax + b}, then y^{'} = [ log (x) - b ] / a

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