Evaluate :

$\text{log 4} + \dfrac{1}{3}\text{ log 125} - \dfrac{1}{5}\text{ log 32}$

Evaluating the expression,

$\Rightarrow \text{log 4} + \dfrac{1}{3}\text{ log 125} - \dfrac{1}{5}\text{ log 32} \\[1em] \Rightarrow \text{log 4} + \dfrac{1}{3}\text{ log 5}^3 - \dfrac{1}{5}\text{ log 2}^5 \\[1em] \Rightarrow \text{log 4 + log (5)}^{\Big(3 \times \dfrac{1}{3}\Big)} - \text{log (2)}^{\Big(5 \times \dfrac{1}{5}\Big)} \\[1em] \Rightarrow \text{log 4 + log 5 - log 2} \\[1em] \Rightarrow \text{log } \dfrac{4 \times 5}{2} \\[1em] \Rightarrow \text{log } \dfrac{20}{2} \\[1em] \Rightarrow \text{log } 10 \\[1em] \Rightarrow 1.$

Hence, $\text{log 4} + \dfrac{1}{3}\text{ log 125} - \dfrac{1}{5}\text{ log 32}$ = 1.