Evaluate the following:

2log 5 + log 8 - $\dfrac{1}{2}$log 4

Given,

$\Rightarrow \text{2log 5 + log 8} - \dfrac{1}{2}\text{log 4} \\[1em] \Rightarrow \text{log 5}^2 + \text{log 8} - \dfrac{1}{2} \times \text{log 2}^2 \\[1em] \Rightarrow \text{log 25 + log 8} - \dfrac{1}{2} \times 2\text{log 2} \\[1em] \Rightarrow \text{log 25 + log 8 - log 2} \\[1em] \Rightarrow \text{log} \dfrac{25 \times 8}{2} \\[1em] \Rightarrow \text{log 100} \\[1em] \Rightarrow \text{log} 10^2 = 2\text{log 10} \Rightarrow 2 \times 1 = 2.$

Hence, $\text{2log 5 + log 8} - \dfrac{1}{2}\text{log 4} = 2.$