Given that log x = m + n and log y = m - n, express the value of log$\Big(\dfrac{10x}{y^2}\Big)$ in terms of m and n.

Given,

$\Rightarrow \text{log }\Big(\dfrac{10x}{y^2}\Big) = \text{log }10x - \text{log } y^2$

= log 10 + log x - 2log y

= 1 + m + n - 2(m - n)

= 1 + m + n - 2m + 2n

= 1 - m + 3n.

Hence, log$\Big(\dfrac{10x}{y^2}\Big)$ = 1 - m + 3n.