(log5)^2 + (log50)(log2)
(log5)^2 + (log(5*10))(log2)
=(log5)^2 + (log5 + log10)(log2)
=(log5)^2 + (log5 + 1)(log2)
=(log5)^2 + (log5)(log2) + log2
=(log5)(log5 + log2) + (log2)
=(log5)(log10) + (log2)
=(log5)(1) + (log2)
=(log5) + (log2)
=(log10)
=1