Example:

Solution:

Use the power rule and the quotient rule to condense to a single logarithm | |

Since both sides of the equation have the same log base the expressions inside the logarithms must be equal | |

Clear the denominator by multiplying by 2 on both sides and simplifying | |

Get x by itself by subtracting 7 on both sides | |

Get x by itself by dividing both sides by negative 1 | |

Check x=13 | |

Check x=1 |

The solution to the equation is x=1.