Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 43

$x\approx0.050$

In exponential form, the given logarithmic equation, $ 5\ln x=-15 ,$ is equivalent to \begin{array}{l}\require{cancel} \ln x=-\dfrac{15}{5} \\\\ \ln x=-3 \\\\ \log_e x=-3 \\\\ x=e^{-3} .\end{array} Hence, the value of the variable that satisfies the given equation is \begin{array}{l}\require{cancel} x\approx0.050 .\end{array}