Question

please can anyone explain me this problem

Answer 1

16.

Given : a^b = b^c = ab.

Let a^b = b^c = ab = k{Some constant}

(i)

⇒ a^b = k

Apply 'log' on both sides, we get

⇒ log(a^b) = log(k)

⇒ b log a = log k  

⇒ log a = log k/b

(ii)

⇒ b^c = k

Apply 'log' on both sides, we get

⇒ log(b^c) = log(k)

⇒ c log b = log k

⇒ log b = log k/c

(iii)

⇒ ab = k

⇒ log(ab) = log (k)

We know that log(ab) = log a + log b

⇒ log a + log b = log k

⇒ (log k/b) + (log k/c) = log k

⇒ log k(1/b + 1/c) = log k

⇒ 1/b + 1/c = 1

⇒ b + c/bc = 1

⇒ b + c = bc.

Therefore, the answer is bc - Option (4).

Hope this helps!