Question

find the indicated value of the logarithmic function.
ln (e^5)
...
the answer is ln (e^5) = \square.

Explanation:

Step1: Recall logarithm property

The natural logarithm $\ln(x)$ and the exponential function $e^x$ are inverse functions. One of the key properties of logarithms is $\ln(e^a) = a$ for any real number $a$, because $\ln$ (which is $\log_e$) and $e^x$ undo each other.

Step2: Apply the property

In the given expression $\ln(e^5)$, we can apply the property $\ln(e^a)=a$ with $a = 5$. So, $\ln(e^5)=5$.

Answer:

5