Question

The equation $x^{x^{x^{...}}}$ = 3 is satisfied when x equal

• A. $\sqrt{3}$
• B. 9
• C. 3
• D. $\sqrt[3]{3}$

Answer 1

Answer: (D)

$\sqrt[3]{3}$

Answer 2

Let $y = x^{x^{x^{...}}}$. Assuming the infinite power tower converges to $y$, the equation can be written as $y = x^y$.

Given that the value of the expression is 3, we have $y=3$.

Substitute $y=3$ into the equation $y = x^y$:

$3 = x^3$

Solve for $x$ by taking the cube root of both sides:

$x = 3^{1/3} = \sqrt[3]{3}$

This value of $x$ is option D.