Black Knight Posted March 12, 2005 Share Posted March 12, 2005 My Pre-Calculus teacher gave us the following problem as a challenge: x^2x=2xthe ^ is raised to the power of (just in case you didn't know)I found that 1/4 was the answer through guess and check but I don't know how to work it! I'm sure it's all just algebra, but I haven't got a clue. Any help would be appriciated.Thanks Link to comment Share on other sites More sharing options...
King Tutankhamun Posted March 12, 2005 Share Posted March 12, 2005 Maybe you want to do logs of each side.So maybe something like this:2xlogx = log2xDon't know if that is how you do it. (probably not) Link to comment Share on other sites More sharing options...
Fire Giant Posted March 12, 2005 Share Posted March 12, 2005 Hmm, my maths application (Derive) calculated for about 200 seconds with no result - therefore, I doubt it's possible to get a numeric solution for it using normal ways of calculating Sure you got the starting formula (x^2x = 2x) right? Link to comment Share on other sites More sharing options...
Bakayaro Posted March 12, 2005 Share Posted March 12, 2005 I gave it a quick hack, but it looks like some intuition is involved anyway.x^(2x) = 2xx^(2x) - 2x = 0x*(x^(2x-1)-2)=0thus...either x = 0or x^(2x-1)=2which means...log2(x)*(2x-1) = 1that makes the guessing a bit easier...but I can't go further from that point. Link to comment Share on other sites More sharing options...
Black Knight Posted March 12, 2005 Author Share Posted March 12, 2005 One of my friends (who is in Calculus), sits around and thinks up math problems. He gave this to his calculus teacher and she couldn't solve it so she gave it to our Pre-Cal teacher and she couldn't solve it either. So she gave it to us! (as if we could solve it!) Anyway he said my answer was right (1/4), but refused to show me the work. Link to comment Share on other sites More sharing options...
Ykkrosh Posted March 12, 2005 Share Posted March 12, 2005 There's another solution at x=1.44373742709798..., which is fairly close to 3^(1/3) (to about one part in a thousand), but I don't know how to get an exact answer. Link to comment Share on other sites More sharing options...
goldenratiophi Posted March 14, 2005 Share Posted March 14, 2005 Mathematica is refusing to give an answer lol. Link to comment Share on other sites More sharing options...
Dnas Posted March 23, 2005 Share Posted March 23, 2005 Hmm.... little problem with x=0.0^(2*0) = undefined Link to comment Share on other sites More sharing options...
Bakayaro Posted March 29, 2005 Share Posted March 29, 2005 That's why I didn't accept x=0 as a solution... did I mention that?oh... whoops... Link to comment Share on other sites More sharing options...
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