A) 5
B) 6
C) 7
D) 8
E) 10
Correct Answer: D
Solution :
\[lo{{g}^{2}}20\text{ }lo{{g}^{2}}80-lo{{g}^{2}}5\text{ }lo{{g}_{2}}320\] \[={{\log }_{2}}({{2}^{2}}\times 5)\,{{\log }_{2}}({{5}^{4}}\times 5)\,-{{\log }_{2}}5\,{{\log }_{2}}\,({{2}^{6}}\times 5)\] \[=(2+{{\log }_{2}}5)\,(4+lo{{g}_{2}}5)-{{\log }_{2}}5(6+{{\log }_{2}}5)\] \[=8+6\,{{\log }_{2}}5+{{({{\log }_{2}}5)}^{2}}-6\,{{\log }_{2}}5-{{({{\log }_{2}}5)}^{2}}\] \[=8\]
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