For base a > 1: $log_a$(f(x)) > $log_a$(g(x)) iff f(x) > g(x) > 0. For base 0 < a < 1: $log_a$(f(x)) > $log_a$(g(x)) iff 0 < f(x) < g(x) (inequality REVERSES). When the base contains a variable, you must consider both cases (base > 1 and base < 1) separately. This is the most common source of JEE errors in logarithmic inequality problems.