Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 36

$x\approx2.463$

In exponential form, the given logarithmic equation, $ \ln (3x) =2 ,$ is equivalent to \begin{array}{l}\require{cancel} \log_e (3x) =2 \\\\ 3x=e^2 .\end{array} Hence, the value of the variable that satisfies the given equation is \begin{array}{l}\require{cancel} x=\dfrac{e^2}{3} \\\\ x\approx2.463 .\end{array}