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Math Help - Precalculus

  1. #1
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    Question Precalculus

    If
    <br />
3^{a} = 4^{b} = 36

    Find
    (2/a) + (1/b).

    I'm studying for a test, and I don't understand this problem at all. Thanks for the help!
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  2. #2
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    Quote Originally Posted by juicysharpie View Post
    If
    <br />
3^{a} = 4^{b} = 36

    Find
    (2/a) + (1/b).

    I'm studying for a test, and I don't understand this problem at all. Thanks for the help!

    3^{a}=36 \iff a=\frac{\ln(36)}{\ln(3)}

    4^{b}=36 \iff b=\frac{\ln(36)}{\ln(4)}

    \frac{2}{\frac{\ln(36)}{\ln(3)}}+\frac{1}{\frac{\l  n(36)}{\ln(4)}}=\frac{2\ln(3)}{\ln(36)}+\frac{\ln(  4)}{\ln(36)}

    =\frac{2\ln(3)+\ln(4)}{\ln(36)}=\frac{\ln(9)+\ln(4  )}{\ln(36)}=\frac{\ln(36)}{\ln(36)}=1
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