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Super Exponentiation Surmise (Posted on 2022-07-31) Difficulty: 2 of 5
Find all real values x that satisfy this equation:
xxx = (1/2)√2

Provide adequate reasoning for your answer.

Note: a^b^c is equal to a^(b^c)《rather than (a^b)^c》

See The Solution Submitted by K Sengupta    
Rating: 4.5000 (2 votes)

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Solution trial and error annotated | Comment 1 of 13
Using Matlab session as a calculator:

>> (1/2)^sqrt(2)             Determines what x^(x^x)  
ans =                             is supposed to look like
         0.375214227246482    
>> x=.9                      First trial
x =
                       0.9
>> x^(x^x)
ans =
         0.908619539138041
>> x=.8
x =
                       0.8
>> x^(x^x)
ans =
         0.829723987624269
>> x=.5
x =
                       0.5
>> x^(x^x)
ans =
         0.612547326536066
>> x=.2                      getting closer
x =
                       0.2
>> x^(x^x)
ans =
         0.311458907098378
>> x=1/4                     (here I've caught on to the surmise)
x =
                      0.25
>> x^(x^x)
ans =
         0.375214227246482 Matches expected value
         
So x = 1/4.         

  Posted by Charlie on 2022-07-31 09:26:33
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