$\huge a^{a^{a^{\cdot^{\cdot^\cdot}}}}=b$

Find the largest real number $b$ such that the above equation has a positive real solution $a$. Approximate $b$ to four significant digits.

If you come to the conclusion that no such value of $b$ exists, enter 666.

**Clarification**: The value of the infinite power tower $\large a^{a^{a^{\cdot^{\cdot^\cdot}}}}$ is defined as the limit of the sequence $x_0=a, x_{n+1}=a^{x_n}$.

×

Problem Loading...

Note Loading...

Set Loading...