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!

Re: Help solving these functions???

what are you trying to solve here? All you've done is define $g(x)$.

Re: Help solving these functions???

Quote:

Originally Posted by

**romsek** 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.

Re: Help solving these functions???

Quote:

Originally Posted by

**IcyJK913** 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)