Product Law

For a>0, a 1 and M,N>0: log_a(MN)=log_a M+log_a N Examples **Expression** | **Simplified form** ln2+ln5 | ln10 log_3 2+log_3 20 | log_3 40 log_2(5x), x>0 | log_2 5+log_2 x The bases must match. Do not split log_a(M+N). For the same base a>0, a 1, and M,N>0: log_a!(MN)=log_a M-log_a N and log_a(Mr)=rlog_a M. A sum inside a logarithm cannot be split. For p,q>0, 3+2lg p-lg q=lg!(1000p2q). Check every original argument before combining.