Sequence And Series Question 188
Question: If $ {\log_{a}}x,\ {\log_{b}}x,\ {\log_{c}}x $ be in H.P., then $ a,\ b,\ c $ are in
Options:
A) A.P.
B) H.P.
C) G.P.
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Here $ \frac{\log x}{\log a},\ \frac{\log x}{\log b},\ \frac{\log x}{\log c} $ are in H.P.
$ \Rightarrow $ $ \frac{\log a}{\log x},\ \frac{\log b}{\log x},\ \frac{\log c}{\log x} $ are in A.P.
$ \Rightarrow $ $ {\log_{x}}a,\ {\log_{x}}b,\ {\log_{x}}c $ are in A.P.
$ \Rightarrow $ $ a,\ b,\ c $ are in G.P. Note: Students should remember this question as a fact.
BETA
