Chapter 9 - Section 9.3 - Logarithmic Functions - 9.3 Exercises: 82

$\frac{1}{3}$

Work Step by Step

For any positive real number $b$ (such that $b\ne1$), we know that $log_{b}b^{r}=r$ (as long as $r\gt0$). For $log_{9}\sqrt[3] 9$: We know that $9^{\frac{1}{3}}=\sqrt[3] 9$, so we can replace $\sqrt[3] 9$ with $9^{\frac{1}{3}}$. Therefore, $log_{9}\sqrt[3] 9=log_{9}9^{\frac{1}{3}}=\frac{1}{3}$.

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