Sequence And Series Question 32
Question: The value of $ x $ satisfying $ {\log_{a}}x+{\log_{\sqrt{a}}}x+{\log_{3\sqrt{a}}}x+………{\log_{a\sqrt{a}}}x=\frac{a+1}{2} $ will be
Options:
A) $ x=a $
B) $ x=a^{a} $
C) $ x={a^{-1/a}} $
D) $ x={a^{1/a}} $
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Answer:
Correct Answer: D
Solution:
$ {\log_{a}}x+2{\log_{a}}x+…….+a{\log_{a}}x=\frac{a+1}{2} $
$ \Rightarrow $ $ {\log_{a}}x(1+2+……..+a)=\frac{a+1}{2} $
$ \Rightarrow $ $ {\log_{a}}x.\frac{a(a+1)}{2}=\frac{a+1}{2} $
$ \Rightarrow $ $ (10^{12}+10^{11}+……+1) $ .
BETA
