Saturday, September 12, 2015

[hiygihed] Variations on the square root of 2

Let q=sqrt(2).

x^2=q ; x = 1.1892071150027210667175

x^q=2 ; x = 1.6325269194381528448

q^q = 1.6325269194381528448

These two values are the same because (q^q)^q = q^(q*q) = q^2 = 2

2^q = 2.66514414269022518865029724987

x^q=q ; x = 1.2777037682648325213

x^x=q ; x = 1.3043511789010365336

x^x=2 ; x = 1.55961046946236935

e^x = 2 ; x = 0.69314718055994530941723212

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