A) \[9-\sqrt{15}\]
B) \[3+\sqrt{15}\]
C) \[2+\sqrt{5}\]
D) \[6-\sqrt{5}\]
Correct Answer: B
Solution :
| We have,\[{{\log }_{(3x-1}})(x-2)=lo{{g}_{(9{{x}^{2}}-6x+1)}}(2{{x}^{2}}-10x-2)\]\[\Rightarrow \]\[{{\log }_{(3x-1)}}(x-2)=lo{{g}_{{{(3x-1)}^{2}}}}(2{{x}^{2}}-10x-2)\] |
| \[\Rightarrow \]\[2{{\log }_{(3x-1)}}{{(x-2)}^{2}}=lo{{g}_{(3x-1)}}(2{{x}^{2}}-10x-2)\]\[\Rightarrow \]\[{{(x-2)}^{2}}=2{{x}^{2}}-10x-2\]\[\Rightarrow \]\[{{x}^{2}}-4x+4=2{{x}^{2}}-10x-2\] |
| \[\Rightarrow \]\[{{x}^{2}}-6x-6=0\]\[\Rightarrow \]\[x=3\pm \sqrt{15}\] |
| \[\therefore \]\[x=3+\sqrt{15},x>2\] |
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