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Find the exact value of x Logarithms

  1. Nov 12, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the exact value of x if:

    2. Relevant equations
    (3x)lg3=(4x)lg4.


    3. The attempt at a solution
    3lg3xlg3=4lg4xlg4
    (xlg3)/(xlg4)=(4lg4)/(3lg3)
    xlg3-lg4=(4lg4)(3-(lg3))
    xlg(3/4)=(4lg4)(3lg(1/3))

    Please help me, Im stuck here!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 12, 2011 #2

    ehild

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    Gold Member

    Re: Logarithms

    Write both sides of the original equation as power of 10, and compare the exponents (which is the same as taking the lg of both sides)
    So you get

    lg(3)lg(3x)=lg(4)lg(4x)

    that is, (lg3)2+(lg3) lg(x)=(lg4)2+(lg4)lg(x)

    Isolate lg(x), use the identity a2-b2=(a-b)(a+b) and simplify. You get lg(x) as the logarithm of a number, from which the exact value of x is found.

    ehild
     
    Last edited: Nov 12, 2011
  4. Nov 12, 2011 #3

    I like Serena

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    Re: Logarithms

    If xa=b, then x=b(1/a).
     
  5. Nov 13, 2011 #4
    Re: Logarithms

    Thank you so much echild. The answer is (1/12)
     
  6. Nov 13, 2011 #5

    ehild

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    Re: Logarithms

    Exactly! Well done!

    ehild
     
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