# 004 Sample Final A, Problem 15

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Solve.

Foundations |
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1) How can we combine the two logs? |

2) How do we remove logs from an equation? |

Answer: |

1) One of the rules of logarithms states that |

2) The definition of the logarithm tells us that if , then . |

Solution:

Step 1: |
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Using a rule of logarithms, the equation becomes . |

Step 2: |
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By the definition of the logarithm, |

means |

Step 3: |
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Now, we can solve for . We have . |

So, there are two possible answers, which are or . |

Step 4: |
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We have to make sure the answers make sense in the context of the problem. Since the domain of the log function is
, -9 is removed as a potential answer. The answer is . |

Final Answer: |
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