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Math Help - Exponential Equation

  1. #1
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    Exponential Equation

    Hi!
    I got a pretty hard problem to solve:
    $${7^x} + {4^x} = {25^x}$$

    I simplified it with $${25^x}$$ and I got:
    $${{{7^x}} \over {{{25}^x}}} + {{{4^x}} \over {{{25}^x}}} = 1$$
    from now on, in my textbook is written to use the monotony of the exponential function in order to solve this, the problem is that I don't really understand what they mean and I would really appreciate if you explain me!
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  2. #2
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    Re: Exponential Equation

    Monoticity of a function refers to whether the function is increasing, decreasing, or constant on an interval. It seems you are trying to solve this equation algebraically, that would be a pain. Is the textbook asking you to solve this algebraically or by means of graphing?
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  3. #3
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    Re: Exponential Equation

    it is not specified, it just suggests to use the monoticity of the exponential function, and I know what monoticity of a function is, the promblem is that I don't really see how it reffers to my problem...
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  4. #4
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    Re: Exponential Equation

    Since the base of the exponent is greater than 1, that means the exponential function will always be increasing for all x. If you are trying to solve this equation, I'd suggest you graph the function asked and look for a point of intersection. Or, bring all terms onto one side of the equation, and find the root of that equation. Using algebra would be too messy and time consuming.
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  5. #5
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    Re: Exponential Equation

    Is the problem to solve the equation or to determine whether or not there is a solution? With f(x)= (7/25)^x+ (4/25)^x, f(0)= 2> 1 and f()= 11/25< 1 so this equation clearly has a root, at approximately x= 1/2, but it is not a rational number and probably not any number that can be reasonably expressed exactly.
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  6. #6
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    Re: Exponential Equation

    yes, the problem is to solve the equation, and there is a solution x=2, but I wanna know how to get to this solution mathematicaly
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  7. #7
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    Re: Exponential Equation

    Exponential Equation-30-12-2012-22-16-14.jpg
    is this the way I should solve it?
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  8. #8
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    Re: Exponential Equation

    Quote Originally Posted by shervlad View Post
    yes, the problem is to solve the equation, and there is a solution x=2, but I wanna know how to get to this solution mathematicaly
    then you must have copied the equation incorrectly ...

    7^2 + 4^2 \ne 25^2
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  9. #9
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    Re: Exponential Equation

    oh, I'm so sorry
    $${7^x} + {24^x} = {25^x}$$
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  10. #10
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    Re: Exponential Equation

    you're not going to solve this algebraically ... one can, however, note that x = 2 is a solution since 7, 24, 25 is a Pythagorean triple.
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