log_a (ab) = c হলে log_b (ab) = ?

প্রশ্ন: log_a (ab) = c হলে log_b (ab) = ?

সমাধান:
দেওয়া আছে,
log_a (ab) = c
⇒ log_a a + log_a b = c
⇒ 1 + log_a b = c
⇒ log_a b = c - 1
⇒ 1/log_b a = c - 1
⇒ logb a = 1/(c -1)

∴ log_b (ab)
= log_b a + log_b b
= {1/(c - 1)} + 1
= (1 + c - 1)/(c - 1)
= c/(c - 1)