Question 3
Consider real numbers $a, b, c$ satisfying $1 \lt b \le c^2 \le a^{10}$, and
$$
\log_a b + 2 \log_b c + 5 \log_c a = 12.
$$
Show that
$$
2 \log_a c + 5 \log_b c + 10 \log_b a \ge 21.
$$
$$
\log_a b + 2 \log_b c + 5 \log_c a = 12.
$$
Show that
$$
2 \log_a c + 5 \log_b c + 10 \log_b a \ge 21.
$$