F-2. Find the value of () (log,,5)(...
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F-2. Find the value of () (log,,5)(log,620) + (109702)2

JEE/Engineering Exams
Maths
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( begin{array}{l}left(log _{10} 5right)left(log _{10} 5 times 4right)+left(log _{10} 2right)^{2} left(log _{10} 1right)left(log _{10} 5+log _{10} 4right)+left(log _{10} 2right)^{2} =left(log _{10} 1right)^{2}+log _{10} 5 log _{10} 2^{2}+left(log _{10} 2right)^{2} =left(log _{10} 5^{2}+2 cdot log _{10} 5 cdot log _{10} 2+left(log _{10} 2right)^{2}right. = & left(log _{10} 5+log _{10} 2right)^{2} =left(log _{10} 5 times 2right)^{2} = & left(log _{10} 10right)^{2} = & (1)^{2} = & 1end{array} )
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