Please find the value of x from the equation: x^(x^(x^(1/3))) = [(X^4)(X^0.5)]^x.

Answer 1

x^(x^(X^(1/3))) = (x^4x)(x^0.5x), so x^(x^(1/3)) = x^(4.5x); x ^(1/3) = 4.5x. Raising both sides to cube:

x = 4.5³x³, x(4.5³ - x²); x ≠ 0. So 4.5³ - x² = 0, x = 4.5^3/2 = 9/2·3√2/2 = 27√2/4.