A) \[1-{{\log }_{2}}3,\,2\]
B) \[{{\log }_{2}}\left( \frac{2}{3} \right)\,,\,\ 1\]
C) \[2,-2\]
D) \[-2,\ 1-\frac{\log 3}{\log 2}\]
Correct Answer: D
Solution :
\[{{2}^{x+2}}{{.3}^{3x/(x-1)}}=9\]Taking log, we get \[(x+2)\log 2+\left( \frac{3x}{x-1} \right)\log 3=2\log 3\] Þ \[(x+2)\left( \log 2+\frac{1}{x-1}\log 3 \right)=0\] Þ \[x=-2\]or \[\frac{1}{1-x}=\frac{\log 2}{\log 3}\] Þ \[1-x=\frac{\log 3}{\log 2}\]Þ\[x=1-\frac{\log 3}{\log 2}\]
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