Use the product rule: (log_b(MN)=log_b M+log_b N)
Use the quotient rule: (log_bleft(frac{M}{N}right)=log_b M-log_b N)
Use the power rule: (log_b(M^k)=klog_b M)
Rewrite radicals as fractional exponents before simplifying
Factor expressions inside the logarithm when possible
Combine like logarithms using the product, quotient, and power rules
Evaluate logs with known values such as (log_b b=1) and (log_b 1=0)
Convert between logarithmic and exponential form when needed
Apply change of base if the base is not convenient
Check that the argument of each logarithm is positive
Use algebra to simplify the expression inside the logarithm first
Expand logarithms only when needed, then simplify terms
Condense multiple logarithms into a single logarithm when possible