perplexus.info :: Just Math : Real Crossed Exponential Puzzle

Real Crossed Exponential Puzzle (Posted on 2024-05-18)

Determine all possible real numbers x, that satisfy this equation:

x^x⁴ = 64

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Solution

Comment 2 of 2 |

I don't need a computer at all!

Just raise each side to the fourth power and arrange the exponents to get (x^4)^(x^4) = 8^8.

Then the obvious solution is x^4=8, which makes x=2^(3/4).

There is the other branch x=-2^(3/4), but that needs to be discarded as x^x^4 is defined over the reals only for positive x.

Posted by Brian Smith on 2024-05-18 22:46:18

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