A) \[{{\log }_{2}}5\]
B) \[_{e}{{\log }_{2}}5\]
C) e
D) 0
Correct Answer: B
Solution :
\[\underset{x\to 1}{\mathop{\lim }}\,({{\log }_{2}}2x\log _{x}^{5})\] \[\underset{x\to 1}{\mathop{\lim }}\,\left[ {{(1+{{\log }_{2}}x)}^{\frac{1}{\log x}}} \right]{{\log }_{2}}x.{{\log }_{x}}5\] \[=e\frac{\underset{x\to 1}{\mathop{\lim }}\,{{\log }_{2}}5}{x+1}\] \[=e{{\log }_{2}}5\]
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