Chapter 4 - Section 4.5 - Exponential and Logarithmic Equations - 4.5 Exercises - Page 447: 43

$x=3$

Changing to exponential form, the given expression, $ \log_4(x^3+37)=3 $ is equivalent to \begin{array}{l}\require{cancel} x^3+37=4^3 \\\\ x^3+37=64 \\\\ x^3=64-37 \\\\ x^3=27 \\\\ x=\sqrt[3]{27} \\\\ x=\sqrt[3]{(3)^3} \\\\ x=3 .\end{array}