perplexus.info :: Just Math : Super Exponentiation Surmise

Super Exponentiation Surmise (Posted on 2022-07-31)

Find all real values x that satisfy this equation:
x^{x^x} = (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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Step by step solution

| Comment 3 of 13 |

(1/2)^sqrt(2)

(1/2)^(2sqrt(2)/2)

((1/2)^2)^(sqrt(2)/2)

(1/4)^(sqrt(2)/2)

(1/4)^(1/sqrt(2))

(1/4)^(2^(-1/2))

(1/4)^((2^2)^(-1/4))

(1/4)^(4^(-1/4))

(1/4)^((1/4)^(1/4)) = x^(x^x)

So 1/4 = x

Posted by Jer on 2022-07-31 10:15:52

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