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Math Help - Help solving these functions???

  1. #1
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    Help solving these functions???

    Hello. I am IcyJK913, and I need help with this problem. I have just finished my freshman year in high school. In the freshman year, I had to take BOTH Algerbra II and Geometry. Next year, I'm going into pre-calculus. The weird thing about me is: I like math. It's just so complex and transcendental that I want to learn it all and possibly major in something (in college) that involves a lot of math, like physics. I want to get ahead though. This year, I've learned everything there is about quadratics and higher-function equations. We didn't get to logarithms or Euler's number, though. But, I am. I understand logarithms completely and I'm a bit iffy on e and ln, but I can make do, and there're these functions I want to solve. I am trying to solve for x (where they touch each other) Please help! ;_;

    f(x) = 2x
    g(x) = x^(f(x))

    When I graph this, I can see two solutions, one of them is (0.25, 0.5), but I just can't find the other one. The last thing I see that I have down is this:

    (ln(y))/(ln(x))

    Please help!
    Last edited by IcyJK913; June 3rd 2014 at 05:58 PM.
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  2. #2
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    Re: Help solving these functions???

    what are you trying to solve here? All you've done is define $g(x)$.
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  3. #3
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    Re: Help solving these functions???

    Quote Originally Posted by romsek View Post
    what are you trying to solve here? All you've done is define $g(x)$.
    I'm sorry. I want to solve for x for when the two lines touch eachother. I have one point where they touch eachother, but I need the other one.
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  4. #4
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    Re: Help solving these functions???

    Quote Originally Posted by IcyJK913 View Post
    I'm sorry. I want to solve for x for when the two lines touch eachother. I have one point where they touch eachother, but I need the other one.
    so the solutions to

    $2x = x^{2x}$

    It has to be solved numerically.

    The answer is approximately (1.44374,2.88747)
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