# Chapter 4 - Section 4.4 - Evaluating Logarithms and the Change-of-Base Theorem - 4.4 Exercises: 46

$5.8$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of logarithms to evaluate the given expression, $\ln e^{5.8} .$ $\bf{\text{Solution Details:}}$ Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 5.8\ln e .\end{array} Since $\ln e=1,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 5.8(1) \\\\= 5.8 .\end{array}

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