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Exponential equation

  1. Oct 16, 2010 #1
    e^2x = 5e^3x


    I understand that I need to take a natural log of both sides here, what I am thrown about is the constant "5". Can I bring that up as an exponent? So, e^2x = e^(3x)^5?
     
  2. jcsd
  3. Oct 16, 2010 #2

    Char. Limit

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    No, not really. That's a rule for logarithms, not for exponents.

    However, it's not really a problem. Once you take the natural log of both sides, you just need to remember a different logarithm rule:

    [tex]log(ab)=log(a)+log(b)[/tex]

    That's all you need here.
     
  4. Oct 17, 2010 #3

    arildno

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    You might also rewrite this equation, dividing with 5e^2x on both sides:
    e^x=1/5
     
  5. Oct 17, 2010 #4
    Sorry but I don't completely follow. I get that I need to take a natural log of both sides, so are you saying: ln(e^2x) = 5 ln(e^2x)?
     
  6. Oct 17, 2010 #5

    Char. Limit

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    No, I'm saying that ln(e^2x)=ln(5e^(3x)). From there, you can use the logarithm rule I posted above to separate the 5.
     
  7. Oct 17, 2010 #6
    Thanks, got it!
     
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