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# Log Properties

### Basic formulas related to logs

Question | Answer |
---|---|

Convert to log: b^y = a | log<b (a) = y |

Convert to log: c^a = t | log<c (t) = a |

Convert to exponential: log<d (a) = b | a^b = d |

Convert to exponential: log<r (x) = y | r^y = x |

log x | log<10 x |

ln x | log<e x |

log a | log<10 a |

ln b | log<e b |

log (ab) | log a + log b |

log (rg) | log (r) + log (g) |

log (a/b) | log (a) - log (b) |

log (h/d) | log (h) - log (d) |

log (n) + log (m) | log (nm) |

log (c) - log (k) | log (c/k) |

log (w) - log (z) | log (w/z) |

log (a^b) | b log (a) |

log (d^c) | c log (d) |

a log (b) | log (b^a) |

k log (d) | log (d^k) |

log<a (a) | 1 |

log<n (n) | 1 |

log<x (x^a) | a |

log<b (b^x) | x |

log<a (1) | 0 |

log<b (1) | 0 |

Change base to d: log<a (b) | log<d (b) / log<d (a) |

Change base to b: log<r (t) | log<b (t) / log<b (r) |

Created by:
lajerauld