be carefull x^x=y^y does not mean in general that x=y for x < 1 x^x has a minimum between 0 and 1 ... left from that minimum and right from that minimum there are couples of x , y and x ! =y where x^x = y^y ... so the last step needs an extra reasoning or justification !
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be carefull x^x=y^y does not mean in general that x=y for x < 1 x^x has a minimum between 0 and 1 ... left from that minimum and right from that minimum there are couples of x , y and x ! =y where x^x = y^y ... so the last step needs an extra reasoning or justification !
eg : (1/2)^(1/2) = (1/4)^(1/4) take ln that gives : 1/2 ln 1/2 for both !
so in general the equation x ( a ^ a ) ^x = 1 leads to a^a = (1/x) ^( 1/x ) for eg a = 1/2 , x=1/2 or x=1/4
Forgot another answer is
X=w(1) /ln(27)
1/3
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No, a^a=b^b, a=b, is not correct. If it were, then 2^2=5^5, 2=5, would be true and 2 not=5.