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in Logarithm by (24.0k points)
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If a, b, c be the pth, qth, rth terms of a GP, then the value of (q – r) log a + (r – p) log b + (p – q) log c is : 

(a) 0 

(b) 1 

(c) –1 

(d) pqr

1 Answer

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by (23.5k points)
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Best answer

(a) 0

Let h be the first term and k be the common ratio of a GP, then 

a = hkp – 1, b = hkq – 1, c = hkr – 1

∴ (q – r) log a + (r – p) log b + (p – q) log c 

= log [hkp –1]q – r + log [hkq –1]r – p + log[hkr –1]p – q 

= log(hq – r + r – p + p – q) (kp – 1)q – r (kq –1)r – p (kr –1)p – q 

= log(ho ko) = log 1 = 0.

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