Question

evaluate the expression without using a calculator.
\ln e^{5}

\ln e^{5} = \square

Explanation:

Step1: Recall the logarithm property

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

Step2: Apply the property to the given expression

In the expression \(\ln(e^5)\), we can identify that \(a = 5\) in the property \(\ln(e^a)=a\). So by applying this property, we get \(\ln(e^5)=5\).

Answer:

\(5\)