# Difference between revisions of "User:Temperal/The Problem Solver's Resource2"

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<math>(a^x)^y=a^{xy}</math> | <math>(a^x)^y=a^{xy}</math> | ||

− | <math>\frac{a^x}{a^y} | + | <math>\frac{a^x}{a^y}=a^{x-y}</math> |

− | < | + | <math>a^0=1</math>, where <math>a\ne 0</math>. |

− | < | + | <math>\log_b xy=\log_b x +\log_b y </math> |

− | < | + | <math>\log_b x^y=y\cdot \log_b x </math> |

− | < | + | <math>\log_b \frac{x}{y} =\log_b x-\log_b y</math> |

− | < | + | <math>\log_b a=\frac{1}{\log_a b}</math> |

− | < | + | <math>\log_b b=1</math> |

− | < | + | <math>\log_b a=\frac{\log_x a}{\log_x b}</math>, where x is a constant. |

− | < | + | <math>\log_1 a</math> and <math>\log_0 a</math> are undefined. |

## Revision as of 17:28, 29 September 2007

## Exponentials and LogarithmsThis is just a quick review of logarithms and exponents; it's elementary content. ## Definitions- Exponentials: Do you really need this one?
- Logarithms: If , . Note that a logarithm in base e, i.e. is notated as , or the natural logarithm of x. If no base is specified, then a logarithm is assumed to be in base 10.
## Rules of Exponentiation and Logarithms
, where .
, where x is a constant. and are undefined. |