Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 40

$x\approx5.521$

In exponential form, the given logarithmic equation, $ \ln (4x-2)=3 ,$ is equivalent to \begin{array}{l}\require{cancel} \log_e (4x-2)=3 \\\\ 4x-2=e^3 .\end{array} Hence, the value of the variable that satisfies the given equation is \begin{array}{l}\require{cancel} 4x=e^3+2 \\\\ x=\dfrac{e^3+2}{4} \\\\ x\approx5.521 .\end{array}