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2^x=12+4x Solve the equation

  1. Aug 27, 2015 #1
    1. The problem statement, all variables and given/known data

    2^x=12+4x Find x.
    2. Relevant equations

    none
    3. The attempt at a solution
    I have tried to change it in form of logarithm xlog2=log4+log3+x and i found that log(3+x) is unexpandable so i was stuck here.
     
  2. jcsd
  3. Aug 27, 2015 #2

    BvU

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    Hello Weiloong, welcome to PF :smile: !

    Your change isn't correctly written: it is true that log(2x) = x log 2, but for log (12 + 4x) you meant log 4 + log(3+x) and that indeed doesn't help all that much.

    Why don't you do some trial and error and see what comes out: x = 1, 2, 3, etc...
     
  4. Aug 27, 2015 #3

    Geofleur

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    You could also try plotting the left and right sides of the equation and seeing where the curves meet, though that only gives an approximate answer.
     
  5. Aug 27, 2015 #4

    berkeman

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    Isn't the Quadratic Equation relevant here? :smile:
     
  6. Aug 27, 2015 #5

    SteamKing

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    I don't think so, since the LHS has 2x rather than x2.
     
  7. Aug 27, 2015 #6

    berkeman

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    Oops, thanks! I misread it. o0)
     
  8. Aug 29, 2015 #7

    HallsofIvy

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    That looks like a candidate for the Lambert W function.
     
  9. Aug 29, 2015 #8

    ehild

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    You can rewrite the equation as x=2(x-2)-3. Both sides are increasing functions. Plotting them, you can see where the roots are. For positive x, it should be greater than 4. If x is negative, it should be near -3. Trial and error will work :)
     
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