Question

WIthout using a calculator, evaluate (lg 5)^2 + lg 2 lg 50

Answer 1

(log 5)^2 + log 2 log 50
= (log 5)^2 + lg 2 (log 5 + log 10)
= (log 5)^2 + lg 2 (log 5 + 1)
= (log 5)^2 + lg 2 * log 5 + log 2
= (log 5)(log 5 + log 2) + log 2
= log 5 log 10 + log 2
= log 5 (1) + log 2
= log 5 + log 2
= log 10
= 1

Answer 2

that is correct, assuming you are using log base 10