Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 33

$x\approx148.413$

In exponential form, the given logarithmic equation, $ \ln x =5 ,$ is equivalent to \begin{array}{l}\require{cancel} \log_e x =5 \\\\ x=e^5 .\end{array} Hence, the value of the variable that satisfies the given equation is \begin{array}{l}\require{cancel} x\approx148.413 .\end{array}