Question

The value of (log₃ 4) (log₄ 5) (log₅ 6) (log₆ 7) (log₇ 8) (log₈ 9) is:
1. 2
2. 7
3. 8
4. 33

Answer 1

Correct Answer - Option 1 : 2

Formula used:

(Loga b) = (log b)/(log a)

log a^b = b log a

Calculation:

(log3 4) (log4 5) (log5 6) (log6 7) (log7 8) (log8 9)

⇒ (log 4 / log 3) × (log 5 / log 4) × (log 6 / log 5) × (log 7 / log 6) × (log 8 / log 7) × (log 9 / log 8)

⇒ (log 9 / log 3)              (∵ Except log 9 and log 3 other terms cancelled out)

We can say log 9 = log₁₀ 9 

So, log 9 = log 3² = 2 log 3

∴ (log 9 / log 3) = 2 log 3/log 3 = 2