Use positive arguments and bases greater than 0 but different from 1. The new base in change of base has the same restrictions. In the power law, \(\log_a(b^n)=n\log_a b\) for&nbsp;\(b&gt;0\).
Product Law : \(\log_{a}{b} + \log_{a}{c} = \log_{a}{(b \times c)}\) Quotient Law : \( \log_{a}{b} - \log_{a}{c} = \log_{a}{ ( b \div c) }\) Power Law : \( \log_{a}{(b^n)} = n\log_{a}{b}\) Change of base : \( \log_{a}{b} = \frac{ \log_{c}{b} }{ \log_{c}{a} } \)

Use positive arguments and bases greater than 0 but different from 1. The new base in change of base has the same restrictions. In the power law, \(\log_a(b^n)=n\log_a b\) for \(b>0\).

**Product Law**: \(\log_{a}{b} + \log_{a}{c} = \log_{a}{(b \times c)}\)
**Quotient Law**: \( \log_{a}{b} - \log_{a}{c} = \log_{a}{ ( b \div c) }\)
**Power Law**: \( \log_{a}{(b^n)} = n\log_{a}{b}\)
**Change of base**: \( \log_{a}{b} = \frac{ \log_{c}{b} }{ \log_{c}{a} } \)

Laws of Logarithms

Exponential and Logarithmic Functions

International Baccalaureate Mathematics: Applications and Interpretation Standard Level