perplexus.info :: Calculus : Powers of powers

Powers of powers (Posted on 2004-05-11)

Solve for x, if:

An algebraic solution is sought!

See The Solution Submitted by Federico Kereki

Rating: 4.1000 (10 votes)

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Puzzle Solution

Comment 13 of 13 |

(In reply to answer by K Sengupta)

Let us solve:

x^(x^3)) =3

=> x^(3*x^3) =3

=> (x^3)^(x^3)=3^3

=> x^3=3

=> x = (3)^(1/3)

Then, the given equation reduces to:

x^(x^3) = 3

=> x =3^((3^(1/3))

Therefore, the required value of x is 3^(cuberoot(3))

Posted by K Sengupta on 2022-12-07 00:48:08

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