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Math Help - Indices, logarithms question

  1. #1
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    Indices, logarithms question

    hey there
    been stuck on this one for ages. can't really get a grasp on it

    Given: 3^x = 4^y = 12^z , show that z = \frac{xy}{x+y}
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  2. #2
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    Re: Indices, logarithms question

    Quote Originally Posted by walleye View Post
    hey there
    been stuck on this one for ages. can't really get a grasp on it

    Given: 3^x = 4^y = 12^z , show that z = \frac{xy}{x+y}
    Here's one way you can do it :
    We know that 3^x = 4^y = 12^z
    now taking logarithms, this equation becomes \implies x\log 3 = y\log 4 = z\log 12
    we also write:  x\log 3 = y\log 4 = z\log 12 = k
    now \log 3=\frac{k}{x} and \log 4=\frac{k}{y}

    Also,  z\log 12 = k \implies z\log(4.3)=k
    by applying the log properties: \implies z\log 4 + z\log 3 = k \implies z(\log 4 +\log 3)=k
    putting in the values of \log 4 and \log 3, \implies zk(\frac{1}{x}+\frac{1}{y})=k
    k gets cancelled,and simplifying gives us: z(\frac{x+y}{xy})=1
    which gives z=\frac{xy}{x+y}


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  3. #3
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    Re: Indices, logarithms question

    Indices, logarithms question-10-aug-2013.png
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