# Difference between revisions of "Logarithm"

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A '''logarithm''' is a shorthand way of expressing [[exponentional notation]]. | A '''logarithm''' is a shorthand way of expressing [[exponentional notation]]. | ||

== Introductory == | == Introductory == | ||

− | The general form for a logarithm can be expressed as <math>log_x y=z</math> which means <math>x^z=y</math>. We would read this as "The logarithm of y base x is z". | + | The general form for a logarithm can be expressed as <math>\log_x y=z</math> which means <math>x^z=y</math>. We would read this as "The logarithm of y base x is z". |

− | We have <math>3^3=27</math>. To express this in [[Logarithmic notation]], we would write it as <math>log_3 27=3</math>. | + | We have <math>3^3=27</math>. To express this in [[Logarithmic notation]], we would write it as <math>\log_3 27=3</math>. |

When a logarithm has no base, it is assumed to be base 10. | When a logarithm has no base, it is assumed to be base 10. | ||

==Logarithmic Properties== | ==Logarithmic Properties== | ||

These hold for all logarithms. | These hold for all logarithms. | ||

− | *<math>log_a b^n= | + | *<math>\log_a b^n=n\log_a b</math> |

− | *<math>log_a b+ log_a c=log_a bc</math> | + | *<math>log_a b+ \log_a c=\log_a bc</math> |

− | *<math>log_a b-log_a c=log_a \frac{b}{c}</math> | + | *<math>\log_a b-\log_a c=\log_a \frac{b}{c}</math> |

− | *<math>(log_a b)(log_c d)= (log_a d)(log_c b)</math> | + | *<math>(\log_a b)(\log_c d)= (\log_a d)(\log_c b)</math> |

− | *<math>\frac{log_a b}{log_a c}=log_c b</math> | + | *<math>\frac{\log_a b}{\log_a c}=\log_c b</math> |

− | *<math>log_a^n b^n=log_a b</math> | + | *<math>\log_a^n b^n=\log_a b</math> |

## Revision as of 20:25, 21 June 2006

A **logarithm** is a shorthand way of expressing exponentional notation.

## Introductory

The general form for a logarithm can be expressed as which means . We would read this as "The logarithm of y base x is z". We have . To express this in Logarithmic notation, we would write it as . When a logarithm has no base, it is assumed to be base 10.

## Logarithmic Properties

These hold for all logarithms.