QuestionFind the value of $\ln e^{4}$ .

Studdy Solution

STEP 1

Assumptions1. We are dealing with natural logarithms, denoted by $\ln$ , which have a base of $e$ (uler's number, approximately equal to.71828). . The property of logarithms $\ln a^b = b \ln a$ is valid.

STEP 2

The given expression is $\ln e^{4}$ . We can apply the property of logarithms $\ln a^b = b \ln a$ to simplify this expression.
$\ln e^{4} =4 \ln e$

STEP 3

The natural logarithm of $e$ is1, that is, $\ln e =1$ . This is because the number $e$ raised to the power of1 gives $e$ itself.
$\ln e = \times1$

STEP 4

Calculate the value of the expression.
$4 \times1 =4$ So, the exact value of the logarithmic expression $\ln e^{4}$ is4.

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