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  4. The solution of log 99 log 2( log 3x) =0 is:

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Q. The solution of $ {{\log }_{99}}\{{{\log }_{2}}({{\log }_{3}}x)\}=0 $ is:

Bihar CECEBihar CECE 2006

Solution:

Given that,
$\log _{99}\left\{\log _{2}\left(\log _{3} x\right)\right\}=0$
$\Rightarrow \log _{2}\left(\log _{3} x\right)=(99)^{0}$
$\Rightarrow \log _{2}\left(\log _{3} x\right)=1$
$\Rightarrow \log _{3} x=2$
$\Rightarrow x=3^{2}=9$