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Question: If *a*, *b*, *c* are in G.P., then \(\log _ { a } x , \log _ { b } x , \log _ { c } x\) are in...

If a, b, c are in G.P., then log⁡ax,log⁡bx,log⁡cx\log _ { a } x , \log _ { b } x , \log _ { c } x are in

A

A.P.

B

G.P.

C

H.P.

D

None of these

Answer

H.P.

Explanation

Solution

a, b, c are in G.P.

⇒ log⁡xa,log⁡xb,log⁡xc\log _ { x } a , \log _ { x } b , \log _ { x } c are in A.P. ⇒ 1log⁡ax,1log⁡bx,1log⁡cx\frac { 1 } { \log _ { a } x } , \frac { 1 } { \log _ { b } x } , \frac { 1 } { \log _ { c } x }

are in A.P.

∴ log⁡ax,log⁡bx,log⁡cx\log _ { a } x , \log _ { b } x , \log _ { c } x are in H.P.