Sequence And Series Question 260
Question: If $ {\log_{x}}y,\ {\log_{z}}x,\ {\log_{y}}z $ are in G.P. $ xyz=64 $ and $ x^{3},\ y^{3},\ z^{3} $ are in A.P., then
Options:
A) $ x=y=z $
B) $ x=4 $
C) $ x,\ y,,z $ are in G.P.
D) All the above
Show Answer
Answer:
Correct Answer: D
Solution:
$ {\log_{x}}y,\ {\log_{z}}x,\ {\log_{y}}z $ are in G.P.
$ \Rightarrow $ $ {{({\log_{z}}x)}^{2}}={\log_{x}}y\times {\log_{y}}z={\log_{x}}z=\frac{1}{{\log_{z}}x} $
$ \Rightarrow $ $ {{({\log_{z}}x)}^{3}}=1 $
$ \Rightarrow $ $ z=x $ Also, we can show $ z=x=y=4 $ .
BETA
