Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

If a, b, c are distinct positive numbers each being different form 1 such that (logb a . logc a - loga a) + (loga b . logc b - logb b) + (loga c . logb c - logc c) = 0, then abc is equal to

1) 0

2) e

3) 1

4) 2

5) 3

Solution: (3) 1

(logb a . logc a – loga a) + (loga b . logc b – logb b) + (loga c . logb c – logc c) = 0

(loga b logc a – 1) + (loga b logc b – 1) = (loga c . loga c – 1) = 0

(logb a . logc a – 1) + (loga b . logc b – 1) = + (loga c . loga c – 1) = 0

(logb a . logc a) + (loga b . logc b) + (loga c . logb c) = 3

(log10 9)3 + (log10 b)3 + (log10 c)3 = 3 log10 a . log10 b . log10 c

If p3 + q3 + r3 = 3pqr then p + q + r = 0

log10 a + log10 b + log10 c = 0

log10 abc = 0

abc = 1

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