Chapter 4 - Section 4.3 - Logarithmic Functions - Summary Exercises on Inverse, Exponential, and Logarithmic Functions - Page 427: 35

$x=5$

Since $y=b^x$ is equivalent to $\log_b y=x,$ then the given equation, $ \log_x \sqrt[3]{5}=\dfrac{1}{3} ,$ is equivalent to \begin{array}{l}\require{cancel} x^{\frac{1}{3}}=\sqrt[3]{5} \\\\ x^{\frac{1}{3}}=5^{\frac{1}{3}} .\end{array} Since the exponents are the same, then the bases can be equated. Hence, \begin{array}{l}\require{cancel} x=5 .\end{array}