Question

evaluate the expression without using a calculator.
\ln e^{6}

\ln e^{6} = \square

Explanation:

Step1: Recall logarithm property

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

Step2: Apply the property

In the expression $\ln(e^6)$, we can apply the property $\ln(e^x)=x$ with $x = 6$. So, $\ln(e^6)=6$.

Answer:

6