Evaluate the following:

2log 2 + log 5 - $\dfrac{1}{2}\text{log 36} - \text{log}\dfrac{1}{30}$

Given,

$\Rightarrow \text{2log 2 + log 5} - \dfrac{1}{2}\text{log 36 - log}\dfrac{1}{30} \\[1em] \Rightarrow \text{2log 2 + log 5} - \dfrac{1}{2} \text{log 6}^2 - \text{(log 1 - log 30)} \\[1em] \Rightarrow \text{2log 2 + log 5} - \dfrac{1}{2} \times 2 \times \text{log 6 - log 1 + log 30} \\[1em] \Rightarrow 2\text{log } 2 + \text{log } 5 - \text{log } 6 - 0 + \text{log } (5 \times 6) \\[1em] \Rightarrow \text{log } 2^2 + \text{log 5 - log 6 + log 5 + log 6} \\[1em] \Rightarrow \text{log 4 + log 5 + log 5} \\[1em] \Rightarrow \text{log } (4 \times 5 \times 5) \\[1em] \Rightarrow \text{log 100} = 2.$

Hence, $\text{2log 2 + log 5} - \dfrac{1}{2}\text{log 36 - log}\dfrac{1}{30}$ = 2.