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  • If a,b,c are in GP then <img alt="\log \frac{1}{a},\log \frac{1}{b},\log \frac{1}{c}" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Clog%20%5Cfrac%7B1%7D%7Ba%7D%2C%5Clog%20%5Cfrac%7B1%

If a,b,c are in GP then \log \frac{1}{a},\log \frac{1}{b},\log \frac{1}{c} are in

Option: 1

GP


Option: 2

HP


Option: 3

AP


Option: 4

AGP


Answers (1)

best_answer

Let common ratio be r

So b = ar,   c = ar2

\log \frac{1}{a}= \log \left ( a \right )^{-1}= -\log a

\log \frac{1}{b}= \log \left ( b \right )^{-1}= -\log b = -\log (ar) = -\log a -\log r

\log \frac{1}{c}= \log \left ( c \right )^{-1}= -\log c = -\log (ar^2) = -\log a -2\log r

Clearly, it is an AP

Thus -\log a,-\log b,-\log c,------ is an AP

 

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