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Formulary: Maths - Algebra - Logarithms

Logarithms

Definitions:

  • a: Real Number a
  • b: Real Number b
  • x: Real Number x

Definition of Logarithms

x = logb( a ) <=> b^x = a    (if a,b>0 and b ≠ 1)


Laws of Logarithms

log(a * b) = log(a) + log(b)

\( {log}\left( {\color{red} {a}} \times {\color{blue} {b}} \right) = {log}\left( {\color{red} {a}} \right) + {log}\left( {\color{blue} {b}} \right) \)


log( a^b ) = b * log(a)

\( {log}\left( {\color{red} {a}}^{\color{blue} {b}} \right) = {\color{blue} {b}} \times {log}\left( {\color{red} {a}} \right) \)


log( a/b ) = log(a) - log(b)

\( {log}\left( \frac{\color{red} {a}}{\color{blue} {b}} \right) = {log}\left( {\color{red} {a}} \right) - {log}\left( {\color{blue} {b}} \right) \)