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Number Powered Cubed Number (Posted on 2024-10-29)

Determine all possible real values of x that satisfy this equation:

   x^x³= 36

No Solution Yet Submitted by K Sengupta

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Solution

| Comment 4 of 7 |

Cube both sides. Then (x^x^3)^3 = (6^2)^3

We can then use exponent rules to rewrite each side. Then (x^3)^(x^3) = 6^6. The obvious solution is then x^3=6, or x=cbrt(6).

x^x is strictly increasing for x>1 so then we know there are no more solutions.

Posted by Brian Smith on 2024-11-03 18:56:03

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