log_10(0.01) = log_10(10^-2) = -2, so x = -2.

log_10(10^x) = x. Therefore, x = 2.

log_10(20) = log_10(2) + log_10(10) = 0.301 + 1 = 1.301.

log_2(8) = 3 and log_2(4) = 2, thus x = 3 + 2 = 5.

log_2(x) + 2 = 6 implies log_2(x) = 4, so x = 2^4 = 16.

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

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

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

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

log_a(64) = 6 implies a^6 = 64. Since 64 = 2^6, we have a = 2.

log_b(25) = 2 implies b^2 = 25. Therefore, b = 5.

log_x(64) = 6 implies x^6 = 64. Since 64 = 2^6, we have x = 2.

log_10(0.01) = log_10(10^-2) = -2.

log_2(1/8) = log_2(2^-3) = -3.

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

log_5(1) = 0 because 5^0 = 1.

log_5(25) = 2, so log_5(25) + log_5(4) = 2 + log_5(4).

log_10(0.01) = log_10(10^-2) = -2.

log_2(32) = log_2(2^5) = 5.

log_10(0.1) = log_10(10^-1) = -1.

log_a(b) + log_a(c) = log_a(bc) by the product property of logarithms.

If a > 1, then log_a(b) < log_a(c) when b < c.

log_a(bc) = log_a(b) + log_a(c) by the product rule of logarithms.