If log₁₀ x = p and log₁₀ y = q, show that xy = (10)^{p + q}.

Given log₁₀ x = a, log₁₀ y = b,

(i) Write down 10^{a + 1} in terms of x.

(ii) Write down 10^2b in terms of y.

(iii) If log₁₀ P = 2a − b, express P in terms of x and y.

Evaluate the following without using log tables :

log 8 + log 25 + 2 log 3 − log 18