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Math Help - Logarithm question

  1. #1
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    Logarithm question

    If X and Y are both positive and log9X=log12Y=log16(X+Y), find the value of X/Y.
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  2. #2
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    Re: logarithm problem

    9, 12 and 16 are base numbers or not?
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  3. #3
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    Quote Originally Posted by yobacul View Post
    9, 12 and 16 are base numbers or not?
    Yes.

    I am trying using the [tex] equation below, hopeful it works.

    If x and y are both positive and \log_9 x = \log_{12} y = \log_{16} (x+y) find the value of x/y.
    Last edited by mr fantastic; October 10th 2009 at 01:21 AM. Reason: Fixed latex
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  4. #4
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    \log_9 x = \log_{12} y = \log_{16} (x+y)
    or

     \frac{log_{10} x}{log_{10} 9}=\frac{log_{10} y}{log_{10} 12}=\frac{log_{10} (x+y)}{log_{10} 16}
    on solving

     \frac{log_{10} x}{log_{10} 9}=\frac{log_{10} (x+y)}{log_{10} 16}

    \frac {log_{10} 16}{log_{10} 9}=\frac{log_{10} (x+y)}{log_{10} x}

    i stuck here
    Last edited by ramiee2010; October 10th 2009 at 06:33 PM. Reason: corrections
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  5. #5
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    Thanks, but I think there is an error as shown below:

    \frac {log_{10} 16}{log_{10} 9}

    is not equal to log_{10}(16-9)
    Last edited by mr fantastic; October 10th 2009 at 09:11 PM. Reason: Fixed the latex
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  6. #6
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    Quote Originally Posted by yeoky View Post
    Thanks, but I think there is an error as shown below:

    \frac {log_{10} 16}{log_{10} 9}

    is not equal to log_{10}(16-9)
    .
    Last edited by mathaddict; October 15th 2009 at 09:31 PM.
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  7. #7
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    Quote Originally Posted by yeoky View Post
    Thanks, but I think there is an error as shown below:

    \frac {log_{10} 16}{log_{10} 9}

    is not equal to log_{10}(16-9)
    Quote Originally Posted by mathaddict View Post
    HI

    It is . What makes you think that it's not ?
    It most certainly is NOT. If it were true then it would also be true that \frac{\log_{10} 100}{\log_{10} 10} = \log_{10}(100 - 10) ....!!
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