Express the following as a single logarithm:

2log 3 - $\dfrac{1}{2}$log 16 + log 12

Given,

$\Rightarrow \text{2log 3} - \dfrac{1}{2}\text{log 2}^4 + \text{log 2}^2.3 \\[1em] \Rightarrow \text{2log 3} - \dfrac{1}{2} \times 4 \times \text{log 2} + \text{log 2}^2 + \text{log 3} \\[1em] \Rightarrow \text{2log 3} - 2\text{log 2} + 2\text{log 2} + \text{log 3} \\[1em] \Rightarrow \text{2log 3 + log 3} \\[1em] \Rightarrow \text{3log 3} \\[1em] \Rightarrow \text{log 3}^3 = \text{log 27}.$

Hence, 2log 3 - $\dfrac{1}{2}$log 16 + log 12 = log 27.