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Math Help - Solving two graphs

  1. #1
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    Solving two graphs

    In an integration exercise, I'm trying to find the points of intersection for two functions. The two functions are:

    d(x) = 3^x
    f(x) = -2x+5

    I set them to being equal, and then took the log of both sides. (The x exponent on 3^x jumps in front because of the logarithm identities)

    3^x = -2x+5
    xlog3 = log(-2x+5)

    Now I am stuck, and I'm not sure of what to do. I would really appreciate anybody's assistance.
    Last edited by ConMan; May 29th 2010 at 10:19 AM.
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  2. #2
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    Quote Originally Posted by ConMan View Post
    3^x = -2x+5
    Cannot be solved using algebra. Numerical solving required...
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  3. #3
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    Quote Originally Posted by ConMan View Post
    In an integration exercise, I'm trying to find the points of intersection for two functions. The two functions are:

    d(x) = 3^x
    f(x) = -2x+5

    I set them to being equal, and then took the log of both sides. (The x exponent on 3^x jumps in front because of the logarithm identities)

    3^x = -2x+5
    xlog3 = log(-2x+5)

    Now I am stuck, and I'm not sure of what to do. I would really appreciate anybody's assistance.
    You can't solve this using algebra but by inspection I find that (1,3) is a point of intersection


    Edit: more info

    The graph of y=3^x is a standard exponential, not dissimilar from e^x. This means it starts off small and quickly expands.

    The graph of y=5-2x is a straight line with a negative gradient, for negative values of x there will be a high value of y.

    Due to these properties (1,3) is the only intersection
    Last edited by e^(i*pi); May 23rd 2010 at 09:31 AM.
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  4. #4
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    Thank you for your timely help.
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