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Math Help - Solving e^{3x}-2e^{-x} = 0.

  1. #1
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    Solving e^{3x}-2e^{-x} = 0.

    Solve this equation

    e^{3x}-2e^{-x} = 0


    I solved in this way, but i dont know if it is correct.

    e^{3x}-2e^{-x} = 0

    e^{3x} = e^{-x} + e^{-x}

    3x + 2x = 0

    x = 0??
    Last edited by mr fantastic; November 13th 2011 at 11:41 AM. Reason: Re-titled.
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  2. #2
    Super Member Quacky's Avatar
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    Re: Solving this equation ?

    I think you mean:

    e^{3x}-2e^{-x}=0

    In which case, multiply through by e^x:

    e^{4x}-2=0

    Which means that e^{4x}=2
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  3. #3
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    Re: Solving this equation ?

    Quote Originally Posted by Fabio010 View Post
    Solve this equation
    e^(3x)-2e^(-x) = 0
    LaTeX tip:
    When an exponent has more that one character use {}.
    [TEX]e^{3x}-2e^{-x} = 0[/TEX] gives e^{3x}-2e^{-x} = 0
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  4. #4
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    Re: Solving this equation ?

    But when i write the function

    e^{4x} = 2

    it is different of the function

    e^{3x} -2e^{-x} = 0


    The solution is the same for y = 0

    but for other numbers like y = -20 it is different
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  5. #5
    Super Member Quacky's Avatar
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    Re: Solving this equation ?

    You started with e^{{\color{red}3}x}-2e^{-x}=0

    When I multiplied through by e^x, it became:

    e^{{\color{red}4}x}-2=0

    The functions are not the same, because I've multiplied through by e^x which is variable. But when you multiply 0 by e^x, the value is still 0 - nothing changes, so the intercept doesn't change.
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  6. #6
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    Re: Solving this equation ?

    Hum ok thanks

    I understood now.. they are the same when x = 0 because e^0 = 1

    Thanks for the help.
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  7. #7
    Super Member Quacky's Avatar
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    Re: Solving this equation ?

    Quote Originally Posted by Fabio010 View Post
    Hum ok thanks

    I understood now.. they are the same when x = 0 because e^0 = 1

    Thanks for the help.
    I'm not sure that's the point I was making. x=0 is not the solution. From where I left off, e^{4x}=2

    Taking natural logs of both sides:

    4x\cdot{ln(e)}=ln(2) and ln(e)=1

    Which makes the solution...
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  8. #8
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    Re: Solving this equation ?

    Quote Originally Posted by Fabio010 View Post
    Solve this equation

    e^{3x}-2e^{-x} = 0


    I solved in this way, but i dont know if it is correct.

    e^{3x}-2e^{-x} = 0

    e^{3x} = e^{-x} + e^{-x}
    This is correct but it's not clear that this helps.

    3x + 2x = 0
    This does not follow at all!

    x = 0??
    Did you not consider checking that answer? If x= 0 then both e^{3x} and e^x are e^0= 1
    Do you beieve that 1- 2= 0?
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