Question

The equationd $x^{x^{x^{+}}}=2$ is satisfied when $x$ is equal to

• A. Infinity
• B. $2$
• C. $\sqrt[4]{42}$
• D. $\sqrt{2}$
• E. None of these

Answer 1

The correct option is D $\sqrt{2}$

If $x^{x^{x^{x^{x^x}}}}=2$, then the exponent, which is again $x^{x^{x^{x^{x^x}}}}$ is also $2$, and we have $x^2=2$. Therefore $x=\sqrt{2}$.