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Math Help - Logs help

  1. #1
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    Logs help

    Given that p=\log_{q}16, express \log_{q}2 and \log_{2}8q in terms of p.

    The answers are \frac{p}{4} and 3+\frac{4}{p} respectively. I kind of get why the first one would be that but I really don't know how to work either of them out
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  2. #2
    Member great_math's Avatar
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    Quote Originally Posted by greghunter View Post
    Given that p=\log_{q}16, express \log_{q}2 and \log_{2}8q in terms of p.

    The answers are \frac{p}{4} and 3+\frac{4}{p} respectively. I kind of get why the first one would be that but I really don't know how to work either of them out
    \log_q2^4=p

    4\log_q2=p

    \log_q2=\frac{p}{4}

    For no. 2)

    Write \log_28q as \log_2(8\cdot q)=\log_28+\log_2q

    \log_28q=3+\frac{1}{\log_q2}

    \log_28q=3+\frac{4}{p}
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