作业帮lg5²+2/3lg8+lg5Xlg20+lg²2等于多少?
来源：学生作业帮助网 编辑：作业帮 时间：2024/10/03 03:40:24
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lg5²+2/3lg8+lg5Xlg20+lg²2等于多少?
lg5²+2/3lg8+lg5Xlg20+lg²2等于多少?
lg5²+2/3lg8+lg5Xlg20+lg²2等于多少?
lg5²+2/3lg8+lg5Xlg20+lg²2
=lg5²+2/3lg2³+lg5Xlg(2²·5)+lg²2
=lg5²+2lg2+lg5X（lg2²+lg5)+lg²2
=(lg25+lg4)+lg²5+2lg5·lg2+lg²2
=lg100+(lg5+lg2)²
=2+(lg10)²
=2+1
=3
原式=2lg5+2lg2+lg5*lg(5*4)+(lg2)^2=2lg5+2lg2+(lg5)^2+2(lg5)*(lg2)+(lg2)^2=2(lg5+lg2)+(lg5+lg2)^2=(lg5+lg2+2)(lg5+lg2)