Given log₁₀a = b, express 10^{2b - 3} in terms of a.

Given log₁₀x = a, log₁₀y = b and log₁₀z = c,

(i) write down 10^{2a - 3} in terms of x.

(ii) write down 10^{3b - 1} in terms of y.

(iii) if log₁₀P = 2a + $\dfrac{b}{2}$ - 3c, express P in terms of x, y and z.

Given log₁₀a = m and log₁₀b = n, express $\dfrac{a^3}{b^2}$ in terms of m and n.

Given log₁₀x = 2a and log₁₀y = $\dfrac{b}{2}$,

(i) write 10^a in terms of x.

(ii) write 10^{2b + 1} in terms of y.

(iii) if log₁₀P = 3a - 3b, express P in terms of x and y.