Question

evaluate the expression without using a calculator.
\\(\ln e^{9}\\)
\\(\ln e^{9} = \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 $\ln(e^9)$, we can see that $x = 9$ in the property $\ln(e^x)=x$. So by applying this property, we get $\ln(e^9)=9$.

Answer:

9