Laws, also called as rules, of logarithm are set of relations which enable us to write logarithmic expressions in different, yet equivalent, ways. Below are the most commonly used rules of logarithm:
Rule 1: loga(MN) = loga(M) + loga(N)
Example: log10(5 × 3) = log10(5) + log10(3)
Rule 2: loga(M/N) = loga(M) – loga(N)
Example: log10(8/9) = log10(8) – log10(9)
Rule 3: loga(M)N = Nloga(M)
Example: log10(4)5 = 5log10(4)
Rule 4: loga(M) = logb(M)/logb(a) (change in base)
Example: log5(6) = log10(6)/log10(5)
Rule 5: loga(A) = 1
These laws are used to simply and/or solve the logarithmic expressions.
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