Determine all possible real numbers x, that satisfy this equation:
xx4 = 64
x^(x^4)=64
(x^4)*log(x)= log(64)
After narrowing down some:
for x=1.681792830:.0000000001:1.681792831
fprintf('%11.9f %11.9f %11.9f\n',x,(x^4)*log(x),log(64))
end
1.681792830 4.158883076 4.158883083
1.681792830 4.158883077 4.158883083
1.681792830 4.158883079 4.158883083
1.681792830 4.158883080 4.158883083
1.681792830 4.158883082 4.158883083
1.681792831 4.158883083 4.158883083 <--------------
1.681792831 4.158883085 4.158883083
1.681792831 4.158883086 4.158883083
1.681792831 4.158883088 4.158883083
1.681792831 4.158883089 4.158883083
1.681792831 4.158883091 4.158883083
Wolfram Alpha identifies 1.681792831 as an approximation to 2^(3/4).
Graphing shows the LHS is monotonically increasing for positive numbers making this the only positive solution.
There are values that seem to meet the requirement around x = -0.515 and x = -0.591, but this is based on a graphing that shows only the real component of what is calculated to be a complex number, in each case.
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Posted by Charlie
on 2024-05-18 21:32:34 |
proposed solution
