Question

evaluate the expression without using a calculator.
\ln e^{3}

\ln e^{3} = \square

Explanation:

Step1: Recall logarithm property

The natural logarithm $\ln x$ and the exponential function $e^x$ are inverse functions. One of the properties of logarithms is $\ln(e^a)=a$ for any real number $a$.

Step2: Apply the property

In the expression $\ln(e^3)$, we can directly apply the property $\ln(e^a) = a$ with $a = 3$. So $\ln(e^3)=3$.

Answer:

$3$