Question 19
(ROM 1) Consider the sequences $(a_n),(b_n)$ defined by
$$a_1=3,\qquad b_1=100,\qquad a_{n+1}=3^{a_n},\qquad b_{n+1}=100^{b_n}.$$
Find the smallest integer $m$ for which $b_m\gt a_{100}$.
$$a_1=3,\qquad b_1=100,\qquad a_{n+1}=3^{a_n},\qquad b_{n+1}=100^{b_n}.$$
Find the smallest integer $m$ for which $b_m\gt a_{100}$.