Step 1: Identify the type — log equation (combine and convert), log inequality (check base for direction), exponential equation (substitute t = $a^x$), functional equation (match pattern). Step 2: For log equations, always verify domain at the end — reject solutions where arguments become non-positive. Step 3: For inequalities with base < 1, flip the inequality immediately and proceed. Step 4: For number-of-digits problems, use floor(n*$log_{10}$(a)) + 1 directly — no need to compute the actual number. Step 5: For functional equations, plug in special values (x=0, y=0, x=y) to determine f(0) and symmetry properties, then identify the function type. Common mistakes: forgetting domain check (costs 4 marks in JEE), wrong inequality direction with base < 1, and treating log($x^2$) = 2*log(x) unconditionally.