Question 131
For every real numbers $1 \lt a \le b \le c$, prove the inequality
$$
\log_a b + \log_b c + \log_c a \le \log_b a + \log_c b + \log_a c. \qquad (D. Tereshin)
$$
$$
\log_a b + \log_b c + \log_c a \le \log_b a + \log_c b + \log_a c. \qquad (D. Tereshin)
$$