(log5)^2+log2·log50

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(log5)^2+log2·log50(log5)^2+log2·log50(log5)^2+log2·log50常用对数一般用lgN表示.(lg5)^2+lg2*lg50=(lg5)^2+lg(10

(log5)^2+log2·log50
(log5)^2+log2·log50

(log5)^2+log2·log50
常用对数一般用 lgN 表示.
(lg5)^2+lg2*lg50
=(lg5)^2+lg(10/5)*lg(10*5)
=(lg5)^2+(lg10-lg5)*(lg10+lg5)
=(lg5)^2+(1-lg5)(1+lg5)
=(lg5)^2+1-(lg5)^2
=1 .

=lg²5+(1-lg5)(1+lg5)
=lg²5+1-lg²5
=1