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

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This is just a quick review of logarithms and exponents; it's elementary content. | This is just a quick review of logarithms and exponents; it's elementary content. | ||

===Definitions=== | ===Definitions=== | ||

− | *Exponentials: Do you really need this one? | + | *Exponentials: Do you really need this one? |

*Logarithms: If <math>b^a=x</math>, <math>\log_b{x}=a</math>. Note that a logarithm in base [[e]], i.e. <math>\log_e{x}=a</math> is notated as <math>\ln{x}=a</math>, or the natural logarithm of x. If no base is specified, then a logarithm is assumed to be in base 10. | *Logarithms: If <math>b^a=x</math>, <math>\log_b{x}=a</math>. Note that a logarithm in base [[e]], i.e. <math>\log_e{x}=a</math> is notated as <math>\ln{x}=a</math>, 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=== | ===Rules of Exponentiation and Logarithms=== | ||

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

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

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

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

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

− | </math>\log_b | + | </math>\log_b b=1<math> |

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

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

## Revision as of 17:27, 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
=a^{x-y}$$ (Error compiling LaTeX. ! Missing $ inserted.)a^0=1a\ne 0\log_b xy=\log_b x +\log_b y $$ (Error compiling LaTeX. ! Missing $ inserted.)\log_b x^y=y\cdot \log_b x $$ (Error compiling LaTeX. ! Missing $ inserted.)\log_b \frac{x}{y} =\log_b x-\log_b y$$ (Error compiling LaTeX. ! Missing $ inserted.)\log_b a=\frac{1}{\log_a b}$$ (Error compiling LaTeX. ! Missing $ inserted.)\log_b b=1$$ (Error compiling LaTeX. ! Missing $ inserted.)\log_b a=\frac{\log_x a}{\log_x b}\log_1 a\log_0 a$ are undefined. |