Properties of Logarithm
Logarithmic Expressions follow different properties. The different properties of logarithms are mentioned below:
Product Formula of Logarithms
Product Formula of logarithm is stated below,
- loga(mn) = logam + logan (Product property)
Quotient Formula of Logarithms
Quotient Formula of logarithm is stated below,
- loga(m/n) = logam – logan (Quotient property)
Power Formula of Logarithms
Power Formula of logarithm is stated below,
- loga(mn) = nlogam (Power property)
Change of Base Formula
Base of the a Lograthin is changed using the formula,
- logba = (logca)/(logcb) (Change of Base Property)
Read More about Change of Base Formula.
Other Logarithm Formulas
Various others Logarithm Formulas are,
- logb(a√n) = 1/a logbn
- log of 1 = loga1 = 0
- logaa = 1 (Identity rule)
- logba= logbc => a= c (Equality rule)
- [Tex]a^{log_ax} [/Tex] = x (Raised to log)
Logarithm Formula
Logarithm was invented in the 17th century by Scottish mathematician John Napier (1550-1617). The Napier logarithm was the first to be published in 1614. Henry Briggs introduced a common (base 10) logarithm. John Napier’s purpose was to assist in the multiplication of quantities that were called sines.
Table of Content
- Logarithm Formula
- Properties of Logarithm
- Product Formula of Logarithms
- Quotient Formula of Logarithms
- Power Formula of Logarithms
- Change of Base Formula
- Other Logarithm Formulas
- Properties of Natural Log
- Product Rule
- Quotient Rule
- Reciprocal Rule
- Log of Power
- Natural Log of e
- Log of 1
- Log Formulas Derivation
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