perplexus.info :: Just Math : Empower With X and 0.4

Empower With X and 0.4 (Posted on 2008-03-10)

Determine all possible positive real numbers X that satisfy this equation:

X^{0.4^X} = 0.4^{X^0.4}

Note: For the purposes of the problem, a^{b^c} is equal to a^(b^c)

Submitted by K Sengupta

Rating: 4.0000 (1 votes)

Solution: (Hide)

X = 0.4 is the only possible real solution to the given problem.

EXPLANATION:

Refer to the explanation as posited by Eigenray in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: solution	K Sengupta	2008-03-21 10:50:29
solution	Eigenray	2008-03-18 18:51:49
re: Not sure if rigorous but...	K Sengupta	2008-03-11 02:52:02
Not sure if rigorous but...	Kenny M	2008-03-10 18:43:24
re: computer exploration (spoiler)	Charlie	2008-03-10 17:42:56
re: computer exploration (spoiler)	Charlie	2008-03-10 16:21:10
computer exploration (spoiler)	Charlie	2008-03-10 16:15:52

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