log_a(25) = log_a(5^2) = 2 log_a(5) = 2p, hence q = 2p.

log_a(bc) = log_a(b) + log_a(c) = p + q.

log_a(bc) = log_a(b) + log_a(c) = p + q.

log_b(27) = 3 implies b^3 = 27 => b = 3.

log_x(16) = 4 implies x^4 = 16 => x^4 = 2^4 => x = 2.

log_x(27) = 3 implies x^3 = 27 => x = 3.

log_x(4) = 2 implies x^2 = 4 => x = 2.

log_x(81) = 4 implies x^4 = 81 => x^4 = 3^4 => x = 3.

log_x(81) = 4 implies x^4 = 81 => x = 3.

Using properties of logarithms, log_3((x + 1)/(x - 1)) = 1 => (x + 1)/(x - 1) = 3 => x + 1 = 3(x - 1) => x = 2.

log_3(x) = 2 implies x = 3^2 = 9.

Using properties of logarithms: log_5((x + 1)/(x - 1)) = 1 => (x + 1)/(x - 1) = 5 => x + 1 = 5(x - 1) => 4x = 6 => x = 2.

log_5(x) = 2 implies x = 5^2 = 25.

log_10(1000) = 3 and log_10(0.01) = -2, thus 3 - 2 = 1.

log_10(1000) = log_10(10^3) = 3.

log_2(32) = 5 and log_2(4) = 2. Therefore, 5 - 2 = 3.

log_2(32) = 5 and log_2(8) = 3. Therefore, 5 - 3 = 2.

log_3(27) = 3 and log_3(9) = 2. Therefore, 3 - 2 = 1.

log_3(81) = log_3(3^4) = 4.

log_4(64) = log_4(4^3) = 3.

log_5(125) = log_5(5^3) = 3.

log_5(25) = 2 and log_5(5) = 1. Therefore, 2 - 1 = 1.

log_a(b^c) = c * log_a(b) by the power rule of logarithms.