Answer
$\frac{1}{7}ln(x)$
Work Step by Step
According to the power rule of logarithms, we know that $log_{b}M^{p}=plog_{b}M$ (when $b$ and $M$ are positive real numbers, $b\ne1$, and $p$ is any real number).
Therefore, $ln(\sqrt[7] x)=ln(x^{\frac{1}{7}})=\frac{1}{7}ln(x)$.
Recall that $ln(x)$ is a natural logarithm with an understood base of $e$.