Since 27 is 3^3, log_3(27) = 3.

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

log_3(9) = 2 and log_3(27) = 3, thus x = 2 + 3 = 5.

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

log_3(x + 1) = 2 implies x + 1 = 3^2 = 9 => x = 8.

log_3(4x) = 2 => 4x = 3^2 = 9 => x = 9/4 = 2.25.

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

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

log_4(16) = log_4(4^2) = 2.

log_4(256) = log_4(4^4) = 4.

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

log_4(x) = 1/2 implies x = 4^(1/2) = 2.

log_4(x) = 2 implies x = 4^2 = 16.

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

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

log_5(25) = 2 and log_5(5) = 1. Therefore, x = 2 + 1 = 3.

log_5(125) = log_5(5^3) = 3. Since log_5(25) = 2, we have x = 2, thus log_5(125) = 3.

log_5(5^x) = x.

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

log_5(x) = 1/2 implies x = 5^(1/2) = sqrt(5).

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

Since 49 = 7^2, log_7(49) = 2, thus x = 2.

log_a(1) = 0 is true for any base a > 0, except when a = 1.

From log_a(16) = 2, we have a^2 = 16, thus a = 4.

log_a(16) = 4 implies a^4 = 16. Since 16 = 2^4, we have a^4 = 2^4, thus a = 2.

log_a(6) = log_a(2 * 3) = log_a(2) + log_a(3) = x + y.

log_a(6) = log_a(2 * 3) = log_a(2) + log_a(3) = x + y.

log_a(3) = 0.5 implies a^0.5 = 3, thus a = 3^2 = 9.

log_a(16) = log_a(4^2) = 2 * log_a(4) = 2 * 2 = 4.

log_a(4) = 2 implies a^2 = 4 => a = 2.