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properties of logarithms

properties of logarithms - Properties of Logarithms...

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Properties of Logarithms Logarithms were introduced about 400 years ago by a mathematician named John Napier. One immediate application of this new idea was to simplify arithmetical computations by changing complex computations into simpler ones. The main computing tool before calculators was the slide rule, which uses properties of logarithms. Other applications include solving exponential equations, modeling real-world behavior, and providing an alternative to the use of linear scales. The basic definitions for common logarithms (logs base ten) and natural logarithms (logs base e) are: y y 10 e y log x log x 10 x y log x lnx e x = = = = = = = = = = = = = . These definitions generate important properties of logarithms, which are a direct result of properties of exponents. The following properties apply to logarithms of all bases. 1. log(AB) log A logB = + 1. ln(AB) lnA lnB = + 2. A B log log A logB     = -     2. A ln ln A lnB B     = -             3.
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