1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook