Given 3(log 5 - log 3) - (log 5 - 2log 6) = 2 - log n, find n.

Given that log₁₀y + 2log₁₀x = 2, express y in terms of x.

If a² = log₁₀x, b³ = log₁₀y and $\dfrac{a^2}{2} - \dfrac{b^3}{3}$ = log₁₀z, express z in terms of x and y.

Given that log m = x + y and log n = x - y, express the value of log m²n in terms of x and y.