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Math Help - How do I write this as a single logarithm?

  1. #1
    Member
    Joined
    Sep 2007
    Posts
    140

    How do I write this as a single logarithm?



    This is what the question reads.

    "Write the following as a single logarithm."

    (4log5x - 2log5y)/ 3log5w
    = (log5x^4 / log5y^2) / log5w^3

    Is that it?

    Or...

    (4log5x - 2log5y)/ 3log5w
    = (log5x^4 / log5y^2) - log5w^3

    I'm a bit confused with this specific problem.
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  2. #2
    Member
    Joined
    Jan 2008
    Posts
    91
    First take the powers leading co-efficients from in front of the logs to get:

    \frac{\log_5 x^4 - \log_5 y^2}{\log_5 w^5}

    Then join the subtraction to get:

    \frac{\log_5 \frac{x^4}{y^2}}{\log_5 w^5}

    Now since they have a common base you can do this:

    \log_{w^5}{\tfrac{x^4}{y^2}}
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