How do I simplify log(a*b) and log(a/b) expressions? I always make sign errors.

Key logarithm rules (for any base): 1) log(ab) = log(a) + log(b). Example: log(6) = log(23) = log2 + log3. 2) log(a/b) = log(a) - log(b). Example: log(3/2) = log3 - log2. (Remember: DIVIDE means SUBTRACT in log). 3) log(a^n) = nlog(a). Example: log(8) = log(2^3) = 3log2. 4) log_a(a) = 1. 5) log_a(1) = 0. 6) Change of base: log_a(b) = log(b)/log(a). Common mistake: log(a+b) is NOT log(a) + log(b). Only multiplication inside becomes addition outside. Sign error fix: log(a/b) — when a/b: the smaller number b is being subtracted. If a>b, log(a/b) > 0. If a<b, log(a/b) < 0.