Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 17

$x\approx4.416$

Taking the logarithm of both sides and using the properties of logarithms, the value of the variable that satisfies the given equation, $ 8^{x-3}=19 ,$ is \begin{array}{l}\require{cancel} \log8^{x-3}=\log19 \\\\ (x-3)\log8=\log19 \\\\ x-3=\dfrac{\log19}{\log8} \\\\ x=\dfrac{\log19}{\log8}+3 \\\\ x\approx4.416 .\end{array}