document.write( "Question 1046218: x^x=100, find x.\r
\n" ); document.write( "\n" ); document.write( "I have tried using newton raphson method but i got stock on the way when lambert w. Function come to play. Please i need the solution as well as lambert w. Function interretation. Thanks in advance \n" ); document.write( "
Algebra.Com's Answer #661708 by rothauserc(4718)\"\" \"About 
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x^x = 100
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\n" ); document.write( "W is the product log or lambert function
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\n" ); document.write( "x = e^(W(2(ln(2)+ln(5))))
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\n" ); document.write( "note that x^x = e^(xlnx) for x>0
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\n" ); document.write( "To get you started
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\n" ); document.write( "If x = W (z), then xe^× = z
\n" ); document.write( "x^x = 100
\n" ); document.write( "xlnx = ln100
\n" ); document.write( "(lnx)e^(lnx) = ln100, I used x = e^(lnx)
\n" ); document.write( "lnx = W(ln100) by definition of W
\n" ); document.write( "x = e^W(ln100)
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\n" ); document.write( "we can graph two equations y=100 and y=x^x
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\n" ); document.write( "\"+graph%28+300%2C+200%2C+-1%2C+4.4%2C+0%2C+250%2C+y=100%2C+x%5Ex%29+\"
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\n" ); document.write( "intersection point is approx 3.6
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