A) \[x>2{{\log }_{2}}5\]or \[x<2{{\log }_{5}}2\]
B) \[{{\log }_{5}}2<x<{{\log }_{2}}25\]
C) \[-{{\log }_{5}}2<x<{{\log }_{2}}25\]
D) \[x<-{{\log }_{5}}4\] or \[x>{{\log }_{2}}5\]
Correct Answer: A
Solution :
(a): \[{{x}^{2}}-\left( {{\log }_{5}}4+{{\log }_{2}}25 \right)x+4>0\] \[\Rightarrow \left( x-2{{\log }_{5}}2 \right)\left( x-2{{\log }_{2}}5 \right)>0\] \[\Rightarrow x\in \left( -\infty ,2{{\log }_{5}}2 \right)\cup \left( 2{{\log }_{2}}5,\infty \right)\]
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