## Logairthms in Base 10

Any number can be written in the formWhenthe number is said to be written in standard form. Powers of 10 are especially important since they are used to estimate orders of magnitude. (Did that man go bankrupt owing millions or tens of millions?).

The relationship between powers of 10 and logarithms in base 10 is illustrated in the following table.

Number | Written as a Power of 10 | |

10,000 | 4 | |

1,000 | 3 | |

100 | 2 | |

10 | 1 | |

0.1 | -1 | |

0.01 | -2 |

This can be extended in a natural way to roots and non – integer powers of 10.

In fact all positive numbers can be written as a power of 10 using the relationship and as a logarithm using the relationshipand any number written in standard form asreturn the logarithm