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Super Exponentiation Surmise II (Posted on 2023-03-01) Difficulty: 3 of 5
Determine all possible real values of X that satisfy this equation:
                              X-X1-X = 2

*** n^n^n is equal to n^(n^n), and NOT (n^n)^n

See The Solution Submitted by K Sengupta    
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Some Thoughts computer exploration | Comment 1 of 2
>> syms x
>> solve(( x^(-(x^(1-x))) ==2),x)
Warning: Unable to solve symbolically. Returning a numeric solution using
vpasolve. 
> In sym/solve (line 304) 
ans =
- 1.309736557638615259713209871911 + 0.40750196122111731029640787257841i
>> 

which Wolfram Alpha does show as causing the expression to evaluate to 2, although Wolfram Alpha could not solve the equation to begin with.

But this is a complex value, not a real value.

  Posted by Charlie on 2023-03-01 14:34:30
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