00:0-1 | in this example , we're given a relation in the | |

00:03 | form of a chart and we're asked to find the | |

00:06 | inverse of the relation . Then graph the relation and | |

00:10 | its inverse to find the inverse of a relation . | |

00:14 | We simply switch the X and Y values in each | |

00:18 | point . In other words , the .1 -4 becomes | |

00:23 | -41 , The .20 become 02 , The .31 becomes | |

00:30 | 1 3 , And the .6 -1 becomes -16 . | |

00:38 | Next we're asked to graph the relation and its inverse | |

00:42 | . So let's first graph the relation Notice that the | |

00:46 | relation contains the points 1 -4-0 3 , 1 and | |

00:52 | 6 -1 . And the inverse of the relation contains | |

00:57 | the points negative 4102 13 and -16 . Finally , | |

01:05 | it's important to understand the following relationship between the graph | |

01:10 | of a relation and its inverse . If we draw | |

01:14 | a diagonal line through the coordinate system , which is | |

01:18 | the line that has the equation , Y equals X | |

01:22 | . Notice that the relation and its inverse are mirror | |

01:26 | images of each other in this line . In other | |

01:29 | words , the inverse of a relation is the reflection | |

01:33 | of the original relation in the line Y equals X | |

00:0-1 | . |

#### DESCRIPTION:

Here were asked to solve for x in the equation: log base x of 144 = 2. Notice that we have a logarithmic equation, so lets first convert the equation to exponential form. Remember that the base of the log represents the base of the power, the right side of the equation represents the exponent, and the number inside the log represents the result, so we have x squared = 144. Now, to solve for x, since x is squared, we simply take the square root of both sides of the equation to get x = plus or minus 12. Remember to always use plus or minus when taking the square root of both sides of an equation. However, notice that x represents the base of the logarithm in the original problem, and the base of a logarithm cannot be negative. Therefore, x cannot be equal to negative 12. So our final answer is x = 12.

#### OVERVIEW:

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