Question

evaluate or simplify the expression without using a calculator.
$ln e^{9x}$
$ln e^{9x} = \square$

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 $\ln(e^y) = y$ for any real number $y$.

Step2: Apply the Property

In the given expression $\ln(e^{9x})$, we can identify that $y = 9x$. Using the property $\ln(e^y)=y$, we substitute $y = 9x$ into the property. So, $\ln(e^{9x}) = 9x$.

Answer:

$9x$