$log_a$(x) = y means $a^y$ = x. Three conditions must hold: (1) base a > 0, (2) base a != 1, (3) argument x > 0. The logarithm is undefined for x <= 0 and for base a = 1 (since 1^y = 1 for all y, no unique solution). In JEE, domain-checking is the #1 skill — most "trap" problems have extraneous solutions that violate x > 0 or the base condition.