Find all real values
x that satisfy this equation:
x
xx = (1/2)
√2
Provide adequate reasoning for your answer.
Note: a^b^c is equal to a^(b^c)《rather than (a^b)^c》
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.
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Posted by Charlie
on 2022-07-31 09:26:33 |
trial and error annotated
