BrainMan Posted February 18, 2004 Share Posted February 18, 2004 Given a>0 solve the equation: xx[a(a+1)]) = a. Link to comment Share on other sites More sharing options...
BrainMan Posted February 18, 2004 Author Share Posted February 18, 2004 To be honest, I think all the superscripts in the problem here is making it harder to read rather than easier. Here is the problem stated wihout the use of superscript: x^x^[a^(a+1)] = a. I dont know. Use whichever seems easiest to look at. Link to comment Share on other sites More sharing options...
aommaster Posted February 18, 2004 Share Posted February 18, 2004 WHOA!!! I have never seen so many indices ever in my life! Where did u get THAT from??! Link to comment Share on other sites More sharing options...
Gampin Posted February 19, 2004 Share Posted February 19, 2004 How did you make that first one? By the way, does anyone know good math forum? Link to comment Share on other sites More sharing options...
neo007 Posted February 20, 2004 Share Posted February 20, 2004 a=1 and x=1 ,seems to work fine Link to comment Share on other sites More sharing options...
Gampin Posted February 20, 2004 Share Posted February 20, 2004 ln a * e^-(a^(a+1)) = x + ln x Link to comment Share on other sites More sharing options...
wolfson Posted February 20, 2004 Share Posted February 20, 2004 Actually to solve x it would go: x = (a^a+1Log(a)/Productlog[a^a+1Log(a)])^a^a-1 Link to comment Share on other sites More sharing options...
BrainMan Posted February 21, 2004 Author Share Posted February 21, 2004 Actually to solve x it would go: x = (a^a+1Log(a)/Productlog[a^a+1Log(a)])^a^a-1 To be quite honest, I'm not sure what Productlog is. How does it relate ot Log or nl? And how did you arrive at this answer? Suppose that a = 1/2. What would Productlog[a^a+1Log(a)] give as a result? Link to comment Share on other sites More sharing options...
wolfson Posted February 21, 2004 Share Posted February 21, 2004 ProductLog is another name for the Lambert W relation. Link to comment Share on other sites More sharing options...
goodyhi11 Posted December 27, 2004 Share Posted December 27, 2004 wow, this problem seem to have some problem. "x^" cannot be followed by "[a^(a+1)]" I'm surprised, not even my super powerful mathematica 5.1 seems to slove it. Link to comment Share on other sites More sharing options...
DimShadow7 Posted December 27, 2004 Share Posted December 27, 2004 Could you show your work to get to the answer? I'm stuck at x * ln x = ln(a) / (a+1) Link to comment Share on other sites More sharing options...
bloodhound Posted December 27, 2004 Share Posted December 27, 2004 i think it would be preferable using LATEX. This is what i get from banging in equation in Maple [math]\exp[{\frac{\mbox{LambertW}(\ln(a)a^{a+1})}{a^{a+1}}][/math] to dimshadow. maple gives this [math]\frac{\ln(a)}{(a+1)\mbox{LambertW}(\frac{ln(a)}{a+1})}[/math] i dont know LW function personally, but u can have a read about it at http://mathworld.wolfram.com/LambertW-Function.html Link to comment Share on other sites More sharing options...
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