Question

高一数学 对数运算

1、lg5²+2/3lg8+lg5*lg20+(lg2)²

2、(lg根号2+lg3-lg根号10)/lg1.8
需要过程！谢谢！

Answer 1

lg5^2+2/3lg8+lg5*lg20+(lg2)^2
=2 lg5+2/3lg2^3+lg5*(lg4+lg5)+(lg2)^2

=2 lg5+(2/3)*3 lg2+lg5*2*lg2+(lg5)^2+(lg2)^2

=2lg5+2lg2+2lg5*lg2+(lg5)^2+(lg2)^2

=2(lg5+lg2)+(lg5+lg2)^2

=2lg10 +(lg10)^2
=2+1
=3
(知道：lgm^n =n*lgm ;完全平方公式：a^2+b^2+2*a*b=(a+b)^2 )

2、
(lg√2+lg3-lg√10)/lg1.8

=(lg√2+lg√9-lg√10)/lg1.8

=[lg√（2*9/10] / lg1.8

=(lg√1.8)/lg1.8

=(1/2)*lg1.8/lg1.8

=1/2

明白：[lgm+lgn=lg(m*n) ;lgm-lgn=lg(m/2) ]

↖(^ω^)↗

Answer 2

1、
lg5²+2/3lg8+lg5*lg20+(lg2)²
=2(1-lg2)+2lg2+(1-lg2)(lg2+1)+(lg2)²
=2-2lg2+2lg2+1-(lg2)²+(lg2)²
=3

2、
(lg√2+lg3-lg√10)/lg1.8
=lg√1.8/lg1.8
=1/2

Answer 3

lg5²+2/3lg8+lg5*lg20+(lg2)²
=2lg5+(2/3)*3lg2+lg5*lg(2*10)+(lg2)²
=2(lg5+lg2)+lg5*(lg2+lg10)+(lg2)²
=2+lg5*lg2+lg5+(lg2)²
=2+lg2*(lg5+lg2)+lg5
2+lg2+lg5
=3

(lg根号2+lg3-lg根号10)/lg1.8
=<lg(3*根号2）-1/2lg10>/lg1.8
=（lg根号18-1/2lg10）/lg1.8
=<1/2(lg18-lg10)>/lg1.8
=1/2lg1.8/lg1.8
=1/2

Answer 4

汗！！！！！！！1