Laws of Logarithms: (1) log_a(mn) = log_a(m) + log_a(n); (2) log_a(m/n) = log_a(m) - log_a(n); (3) log_a(m^n) = n × log_a(m); (4) Change of base: log_a(b) = log_c(b)/log_c(a); (5) log_a(a) = 1; (6) log_a(1) = 0. Application: log(1000) = log(10^3) = 3 log(10) = 3. Or log_2(32) = log_2(2^5) = 5. Solving: Break down complex arguments using product/quotient rules. Shortcut: Convert to common base before applying laws. Exam tip: Law of exponents parallels logarithm laws. Practice: Solve log_a(x) = 3 means x = a^3. Verify solutions by converting back to exponential form.