If M and N are positive real numbers and a is a positive number other than 1 then:
1. logₐMN = logₐM + logₐN
2. logₐM/N = logₐM - logₐN
3. logₐM = logₐN if and only if M = N
4. logₐM^k = klogₐM for any real number k. use when solving an exponential.
Ex 1. log(MN)^2 = 2logM + 2logN
Ex 2. logM/N^2 = logM - 2logN
Ex 3. log M^3N/2 = 3logP + logN - log2
Ex 4. logMsqrtN/B = logMN^1/2 / B
= logM + 1/2logN - logB
Ex 5. log1/M = log1 - logM
Ex 6. log2 + log3 + log4 = log25
Ex 7. log8+ log5 - log4 = log40/4 = log10
Ex 8. 1/2log9 + log5 = log3 + log5 = log15
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