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).