# Chapter 4 - Section 4.5 - Exponential and Logarithmic Equations - 4.5 Exercises - Page 447: 35

$x=e^2$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $5\ln x=10 ,$ convert it to exponential form. $\bf{\text{Solution Details:}}$ Dividing both sides by $5 ,$ the equation above is equivalent to \begin{array}{l}\require{cancel} \ln x=\dfrac{10}{5} \\\\ \ln x=2 .\end{array} Since $\ln x=\log_e x,$ the equation above is equivalent to \begin{array}{l}\require{cancel} \log_e x=2 .\end{array} Since $y=b^x$ is equivalent to $\log_b y=x,$ the exponential form of the equation above is \begin{array}{l}\require{cancel} e^2=x \\\\ x=e^2 .\end{array}

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