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Logarithm Proof

  1. Dec 1, 2008 #1
    1. The problem statement, all variables and given/known data


    1/log3a + 1/log4a = 1/log12a

    2. Relevant equations

    Logarithms rules (addition, subtraction, power, etc.)


    3. The attempt at a solution

    Left Side:

    1/log3a + 1/log4a
    =log3a+log4a/log12a (via common denominator)

    The problem is how to add logarithms with different bases. I tried converting the log3a to log4a (I get log4a/log43). After that, I subbed it back into the equation.


    But I don't think that gets me anywhere...

    Right side still remains the same (1/log12a)

    Any help is appreciated! Thanks in advance :).

    P.S. What program do people use to make their equations look so neat (the fraction looks real - ex. 1/4 really looks like 1 (horizontal line) 4)?
  2. jcsd
  3. Dec 1, 2008 #2


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    Science Advisor
    Homework Helper

    Let's just convert everything to a single log base, like log_12. E.g. log_3(a)=log_12(a)/log_12(3).
  4. Dec 1, 2008 #3
    Oh, wow. Sigh, I hate it when you take the wrong approach in proving Left Side equals Right Side.

    Thanks for the help! Can't believe it was so simple after your suggestion :).
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