A) \[{{10}^{\sqrt{2}}}\]
B) 10
C) \[{{10}^{4}}\]
D) None of these
Correct Answer: B
Solution :
[b] Given, \[{{T}_{4}}=200\] |
\[\Rightarrow {{\,}^{6}}{{C}_{3}}{{\left( \sqrt{{{x}^{\left( \frac{1}{\log \,\,x+1} \right)}}} \right)}^{3}}{{({{x}^{1/12}})}^{3}}=200\] |
\[\Rightarrow 20.{{x}^{\frac{3}{2(log\,x+1)}+\frac{1}{4}=}}200\] |
\[\Rightarrow {{x}^{\left\{ \frac{3}{2(log\,x+1)}+\frac{1}{4} \right\}}}=10\] |
\[\Rightarrow \,\,\,\frac{3}{2(\log \,x+1)}+\frac{1}{4}\,\,=\,{{\log }_{x}}10=\frac{1}{{{\log }_{10}}x}\] |
\[\Rightarrow \frac{3}{2(y+1)}+\frac{1}{4}=\frac{1}{y}\] where \[y={{\log }_{10}}x\] |
\[\Rightarrow y=-4\] or \[y=1\] |
\[\Rightarrow {{\log }_{10}}x=-4\] or \[\Rightarrow {{\log }_{10}}x=1\] |
\[\Rightarrow x={{10}^{-4}}\] or \[10\Rightarrow x=10(\because \,x>1)\] |
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