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Math Help - Proving a log identity

  1. #1
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    Proving a log identity

    Hey guys!

    I need help proving this log identity:
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  2. #2
    Member kjchauhan's Avatar
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    \frac{3}{\log_{2}a}-\frac{2}{\log_{4} a}

    Change the base of all
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  3. #3
    Member kjchauhan's Avatar
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    \frac{3}{\frac{\log_{\frac{1}{2}}a}{\log_{\frac{1}  {2}}2}}-\frac{2}{\frac{\log_{\frac{1}{2}}a}{\log_{\frac{1}  {2}}4}}

    =\frac{3 \log_{\frac{1}{2}}2}{\log_{\frac{1}{2}}a}-\frac{2 \log_{\frac{1}{2}}4}{\log_{\frac{1}{2}}a}

    =\frac{ \log_{\frac{1}{2}}2^3 - \log_{\frac{1}{2}}2^4}{\log_{\frac{1}{2}}a}

    =\frac{ \log_{\frac{1}{2}}{\frac{2^3}{2^4}}}{\log_{\frac{1  }{2}}a}

    =\frac{ \log_{\frac{1}{2}}{\frac{1}{2}}}{\log_{\frac{1}{2}  }a}

    =\frac{ 1}{\log_{\frac{1}{2}}a}
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  4. #4
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    thanks alot !!!! really appreciate it i spent forever on that question.
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