Evaluate the following:

log$(10 ÷ \sqrt[3]{10})$

Given,

$\Rightarrow \text{log}(10 ÷ \sqrt[3]{10}) \\[1em] \Rightarrow \text{log}\Big(\dfrac{10}{\sqrt[3]{10}}\Big) \\[1em] \Rightarrow \text{log}\Big(\dfrac{10}{10^{\dfrac{1}{3}}}\Big) \\[1em] \Rightarrow \text{log}(10)^{1 - \dfrac{1}{3}} \\[1em] \Rightarrow \text{log}(10)^{\dfrac{2}{3}} \\[1em] \Rightarrow \dfrac{2}{3}\text{log 10} \\[1em] \Rightarrow \dfrac{2}{3}.$

Hence, $\text{log}(10 ÷ \sqrt[3]{10}) = \dfrac{2}{3}$.