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Natural log helpp

  1. Sep 8, 2011 #1
    natural log helpp!!

    1. The problem statement, all variables and given/known data
    ln(x+10)+ln(x+4)=2



    2. The attempt at a solution

    okay so i took it down to (-14+-(14^2 - 4(e^2 - 40))^1/2) / 2

    which i broke down to 356 - 4e^2 inside the sqrt.

    am i on the right track and if so Whats the next step?
     
  2. jcsd
  3. Sep 8, 2011 #2

    wukunlin

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    Gold Member

    Re: natural log helpp!!

    looks ok, I'm not sure what you mean by next step though
    x = (-14+-(14^2 - 4(e^2 - 40))^1/2) / 2 is your answer
     
  4. Sep 8, 2011 #3
    Re: natural log helpp!!

    it can be broken down further into something more simplified.

    the example i have goes down from x^2 + 4x -(e^2 + 5)=0

    to x= -2+-sqrt 9+e^2

    but it doesnt show the steps used
     
  5. Sep 8, 2011 #4
    Re: natural log helpp!!

    i figured it out. the answer was -7+ (9+e^2)^1/2
     
  6. Sep 10, 2011 #5
    Re: natural log helpp!!

    ln(x+10)+ln(x+4)=2
    ln[(x+10)(x+4)] = 2
    (x+10)(x+4) = e^2
    x^2 + 14x + 40 = e^2
    x^2 + 14x + 40-e^2 = 0
    x = ( -14 +- sqrt((14^2)-4*1*(40-e^2)) ) / (2) [quadratic formula]
    x = answer
     
  7. Sep 10, 2011 #6

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: natural log helpp!!

    No. if you take the negative in the "+-", you get a number less than -10 so that both x+10 and x+ 4 are negative and you cannot take the logarithm.

    Only ( -14 + sqrt((14^2)-4*1*(40-e^2)) ) / (2) satifies the original equation.
     
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