A) 1
B) 2
C) 3
D) 4
Correct Answer: A
Solution :
\[{{\log }_{4}}\left\{ \,{{\log }_{2}}(\sqrt{x+8}-\sqrt{x}) \right\}=0\] \[\Rightarrow {{4}^{0}}={{\log }_{2}}\left( \sqrt{x+8}-\sqrt{x} \right)\] \[\Rightarrow {{2}^{1}}=\sqrt{x+8}-\sqrt{x}\] \[\Rightarrow 4=x+8+x-2\sqrt{{{x}^{2}}+8x}\] \[\Rightarrow 2\sqrt{{{x}^{2}}+8x}=2x+4\] \[\Rightarrow {{x}^{2}}+8x={{x}^{2}}+4+4x\] \[\Rightarrow 4x=4\] \[\Rightarrow x=1\].You need to login to perform this action.
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