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Homework Help: Logarithms STUCK

  1. Feb 3, 2010 #1
    logarithms STUCK!!

    8logx-3logx^2 = log8x - log4x

    im struggling to find x. my working out so far is:

    rhs log8x-log4x

    = log2

    = 8logx - 3logx^2 = log 2

    = 8logx - 3logx^2 - log 2 = 0

    = -b+ or - the square root of b^2-4ac divided by 2a

    a = -3 b = 8 c = - 2

    = -8 + or - sqaure root of 8^2 (-4x-3x^2-2) divided by 2x - 3^2

    x= -8 + or - square root of 64 - 24 divided by -6

    = square of 40 divided by -6

    = -8 + or - 6.3245 divided by -6

    = - 8 + or - , -1.05408

    x= -9.0540
    x= 6.94592

    can anyone help me. am stuck and cant see where ive gone wrong
     
  2. jcsd
  3. Feb 3, 2010 #2

    HallsofIvy

    User Avatar
    Science Advisor

    Re: logarithms STUCK!!

    Surely this is supposed to be log(x^2), not (log x)^2 so this is NOT a quadratic equation.

    log(x^2)= 2log(x) so you have 8log(x)- 6 log(x)= 2log(x)= log 2.

    2lo(x)= log(x^2)= log(2) so x^2= 2.

     
  4. Feb 3, 2010 #3

    Mark44

    Staff: Mentor

    Re: logarithms STUCK!!

    You're treating the equation below as a quadratic equation. It's not, so you can't use the Quadratic Formula.
    Incidentally, don't connect equations with =. Instead, use "implies" - ==> or "is equivalent to" - <==>.
    8logx-3logx2 = log8x - log4x
    ==> 8logx-3logx2 = log2

    In the next step replace 8logx and 3logx2 by different expressions using one of the properties of logarithms. In each case you should get log <something>, with no coefficient in front of log.

    In the step after that combine log <A> - log<B> into a single log expression. A and B are the "somethings" you get in the previous step.

    If all goes well, you should end up with an equation that looks like this:
    log<something else> = log 2.

    If log a = log b, what can you say about a and b?
     
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