For nested logs like log_a(log_b(x)), work from inside out. Example: log_2(log_3(81)) = log_2(4) = 2 (since log_3(81) = 4). For equations: log_3(log_2(x)) = 1 means log_2(x) = 3, so x = 8. Domain is critical: the inner log must be positive for the outer log to exist, so log_b(x) > 0 requires x > 1 (for b > 1).