计算4lg2+3lg5-lg1/5(1)4lg2+3lg5-lg1/5(2)lg12.5-lg5/8+lg1/2(3)lg²4+lg²25+8lg2*lg5

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/03 09:12:25
计算4lg2+3lg5-lg1/5(1)4lg2+3lg5-lg1/5(2)lg12.5-lg5/8+lg1/2(3)lg²4+lg²25+8lg2*lg5

计算4lg2+3lg5-lg1/5(1)4lg2+3lg5-lg1/5(2)lg12.5-lg5/8+lg1/2(3)lg²4+lg²25+8lg2*lg5
计算4lg2+3lg5-lg1/5
(1)4lg2+3lg5-lg1/5
(2)lg12.5-lg5/8+lg1/2
(3)lg²4+lg²25+8lg2*lg5

计算4lg2+3lg5-lg1/5(1)4lg2+3lg5-lg1/5(2)lg12.5-lg5/8+lg1/2(3)lg²4+lg²25+8lg2*lg5
4lg2 +3lg5-lg(1/5)
=lg16+lg125-lg(1/5)
=lg[16×125÷(1/5)]
=lg(16×125×5)
=lg10000
=4
lg12.5-lg(5/8)+lg(1/2)
=lg[12.5÷(5/8)×(1/2)]
=lg[(25/2)×(1/2)×(8/5)]
=lg[(25/4)×(8/5)]
=lg10
=1
(lg4)^2 +(lg25)^2 +8lg2lg5
=(2lg2)^2 +(2lg5)^2 +8lg2lg5
=(2lg2+2lg5)^2
=(2lg10)^2
=4