3. Let $f(x)=\ln x$. What are the values of $x$ in the domain of $(f \circ f \circ f \circ f \circ f)(x)$ ?
Answer: $x>e^{e^{e}}$
Solution: We have $(f \circ f \circ f \circ f \circ f)(x)=\ln (\ln (\ln (\ln (\ln (x)))))$. The domain of this function must satisfy $\ln (\ln (\ln (\ln (x))))>0$ which implies that $\ln (\ln (\ln (x)))>1, \ln (\ln (x))>e, \ln (x)>e^{e}$ and $x>e^{e^{e}}$.