All real logarithms below have positive arguments and a positive base different from 1. In the power law, the argument before raising it to a power is positive. Statements labelled as common mistakes describe rules that are not identities; equality can still occur for particular allowed values.
Product Law:
\({{\log }_{a}}b+{{\log }_{a}}c={{\log }_{a}}\left( b\times c \right)\)
e.g. \(\ln 2+\ln5=\ln10\) , \({{\log }_{3}}2+{{\log }_{3}}20={{\log }_{3}}40\), \({{\log }_{2}}3+{{\log }_{2}}7+{{\log }_{2}}2={{\log }_{2}}42\)
Important notes:
The formula \({{\log }_{a}}(p+q)= \left( \log_ap \right)\left( \log_aq \right)\) is not an identity.

All real logarithms below have positive arguments and a positive base different from 1. In the power law, the argument before raising it to a power is positive. Statements labelled as common mistakes describe rules that are not identities; equality can still occur for particular allowed values.

\({{\log }_{a}}b+{{\log }_{a}}c={{\log }_{a}}\left( b\times c \right)\)

e.g. \(\ln 2+\ln5=\ln10\) , \({{\log }_{3}}2+{{\log }_{3}}20={{\log }_{3}}40\), \({{\log }_{2}}3+{{\log }_{2}}7+{{\log }_{2}}2={{\log }_{2}}42\)

The formula \({{\log }_{a}}(p+q)= \left( \log_ap \right)\left( \log_aq \right)\) is not an identity.

Question 115731

Question 115731

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