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)

See The Solution Submitted by K Sengupta

Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Not sure if rigorous but...

| Comment 4 of 7 |

take the 0.4th root of both sides:

x^0.4^(x/0.4) = 0.4^x

then take the xth root of both sides

x^0.4^(x/0.4/x)=.4

but the LHS reduces to X^1

therefore x=0.4!

Posted by Kenny M on 2008-03-10 18:43:24

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