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Logarithms with a twist

  1. May 5, 2016 #1
    MENTOR note: THread moved from General Math

    I just can get it

    This problem has been driving me crazy for a week now

    [tex]If\quad a,b,c\quad \neq \quad 1\\ Also\quad (log_{ b }{ a\cdot }log_{ c }{ a }\quad +\quad log_{ a }{ a })\quad +\quad (log_{ a }{ b\cdot }log_{ c }{ b }\quad +\quad log_{ b }{ b })\quad +\quad (log_{ a }{ c\cdot }log_{ b }{ c }\quad +\quad log_{ c }{ c })\quad =\quad 0\\ Prove\quad that\quad \\ abc\quad =\quad 1\\ Additionally\\ If\quad a,b,c\quad =\quad 1\quad Prove\quad a=b=c[/tex]


    My attempt

    So what I did was

    call log_a b = p ,log_b = q,log_c a=q

    I plugged this in and made an interesting discovery

    pqr = 1

    So i used this in the equation above and tried to get to the proof but didn't work

    Where am I faltering
    ?
     
  2. jcsd
  3. May 5, 2016 #2

    jedishrfu

    Staff: Mentor

    On the first proof, did you notice how to simplify the ##log_{a} ( a )##?
     
  4. May 5, 2016 #3
    Of course i wrote it as 1 and proceeded
     
  5. May 5, 2016 #4

    jedishrfu

    Staff: Mentor

    Did you try to convert the factors to a common log base base like log_b(a) + ln(a)/ln(b)?
     
  6. May 5, 2016 #5
    Yes i did try that
     
  7. May 5, 2016 #6

    jedishrfu

    Staff: Mentor

    and will you be showing your work? We can't help you here unless you show some work.
     
  8. May 5, 2016 #7
    Well its alright i got it on my own:smile:
     
  9. May 5, 2016 #8

    jedishrfu

    Staff: Mentor

    so what was the trick you needed?
     
  10. May 5, 2016 #9
    I needed to remember that If a3 + b3 + c3 = 3abc

    a+b+c=0 or a=b=c
     
  11. May 5, 2016 #10

    jedishrfu

    Staff: Mentor

    Where did that come from? It wasn't part of the original problem you posted.
     
  12. May 5, 2016 #11

    haruspex

    User Avatar
    Science Advisor
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    2016 Award

    Shouldn't there be a minus sign in there?
     
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