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Thread: 3^x = 4^y = 12^z

  1. #1 3^x = 4^y = 12^z 
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    Greetings, I have an equations that needed to be proved.
    3^x = 4^y = 12^z

    show that z = (xy)/(x+y) from the above equation


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    • #2 Re: 3^x = 4^y = 12^z 
      . DrRocket's Avatar
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      Quote Originally Posted by TzerMaan
      Greetings, I have an equations that needed to be proved.
      3^x = 4^y = 12^z

      show that z = (xy)/(x+y) from the above equation
      This is pretty clearly homework. We won't do your work for you.

      You have also neglected the solution x=y=z=0.


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    • #3  
      Forum Ph.D. Heinsbergrelatz's Avatar
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      i hope its not homework, so having that said, i will help you.

      you have to make use of logarithms.

      so you have two equations,




      so taking log, (i assume you have knowledge in logarithms)

      xlog3=ylog4-----------1
      ylog4=zlog12-----------2

      now if we see equation 2, it becomes;





      now we know that log3=ylog4/x
      so if we substitute this in to equation2,





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