Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 19

$x\approx3.912$

Taking the natural logarithm of both sides and using the properties of logarithms, the value of the variable that satisfies the given equation, $ e^x=50 ,$ is \begin{array}{l}\require{cancel} \ln e^x=\ln50 \\\\ x\ln e=\ln50 \\\\ x(1)=\ln50 \\\\ x=\ln50 \\\\ x\approx3.912 .\end{array}