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If $\log (a + c) + \log (a + c - 2 b) = 2 \log (a - c)$ then

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a, b, c are in A.P.

a, b, c are in G.P

a, b, c are in H.P

b + c, c + a, a + b are in H.P

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detailed solution

Correct option is C

Given equation implies(a+c)(a+c−2b)=(a−c)2⇒(a+c)2−(a−c)2=2b(a+c)⇒ 4ac=2b(a+c)⇒b=2aca+c⇒a,b,c are in H.P.

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If log⁡(a+c)+log⁡(a+c−2b)=2log⁡(a−c) then

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If $\log (a + c) + \log (a + c - 2 b) = 2 \log (a - c)$ then