My Math Forum can anyone solve this??

 Algebra Pre-Algebra and Basic Algebra Math Forum

 April 23rd, 2014, 04:07 AM #1 Newbie   Joined: Apr 2014 From: new york Posts: 3 Thanks: 0 can anyone solve this?? hello... i wanted to know if anyone can solve this : X^X=64
 April 23rd, 2014, 04:38 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra What is the problem you have with it? Without some idea of what you are finding difficult,, it's hard to know how to explain it.
 April 23rd, 2014, 04:42 AM #3 Senior Member     Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra You need the Lambert W function $W$ defined as $z=W(z)e^{W(z)}$ for $z\in\mathbb C$. Thus $\displaystyle 64\,=\,x^x$ $\displaystyle \ln64\,=\,x\ln x\,=\,(\ln x)e^{\ln x}$ So $\displaystyle W(\ln64)\,=\,\ln x$ $\displaystyle \implies$ $\displaystyle x\,=\,e^{W(\ln64)}$. Thanks from agentredlum and topsquark
 April 23rd, 2014, 04:44 AM #4 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 There is no closed form in general. Lambert W function - Wikipedia, the free encyclopedia Scroll down to example 2. I learned this from Mr. TNT (mathbalarka)
 April 23rd, 2014, 04:50 AM #5 Newbie   Joined: Apr 2014 From: new york Posts: 3 Thanks: 0 anybody can find that number...it can be a "Square root" or periodic number... the closest one is (√11.556)

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