# Logarithmic Functions

The **logarithmic function** in base **a** is the **inverse function** of the **exponential function** in base **a**.

x | |
---|---|

1/8 | -3 |

1/4 | -2 |

1/2 | -1 |

1 | 0 |

2 | 1 |

4 | 2 |

8 | 3 |

x | |
---|---|

1/8 | 3 |

1/4 | 2 |

1/2 | 1 |

1 | 0 |

2 | −1 |

4 | −2 |

8 | −3 |

# Properties of Logarithmic Functions

It is continuous.

The points (1, 0) and (a, 1) belong to the graph.

Increasing if a > 1.

Decreasing if a < 1.

The graph of the logarithmic function is symmetrical (with respect to the bisector of the 1st and 3rd quadrant) to the graph of the exponential function as they are the inverse functions of each other.