If log₁₀ 2 = a and log₁₀ 3 = b; express log $2\dfrac{1}{4}$ in terms of 'a' and 'b'.

Given,

log₁₀ 2 = a and log₁₀ 3 = b

Simplifying the expression :

$\Rightarrow \text{log } 2\dfrac{1}{4} \\[1em] \Rightarrow \text{log } \dfrac{9}{4} \\[1em] \Rightarrow \text{log 9 - log 4} \\[1em] \Rightarrow \text{log 3}^2 - \text{log 2}^2 \\[1em] \Rightarrow \text{2 log 3 - 2 log 2} \\[1em] \Rightarrow \text{2b - 2a}.$

Hence, $\text{log } 2\dfrac{1}{4}$ = 2b - 2a.