对数的运算化简:1 lg5方+(2/3)lg8+lg5lg20+(lg2)方 2 (log2 5+log4 0.2)(log5 2+log25 0.5)
问题描述:
对数的运算
化简:1 lg5方+(2/3)lg8+lg5lg20+(lg2)方
2 (log2 5+log4 0.2)(log5 2+log25 0.5)
答
1 =2lg5+lg4+lg5(lg2+lg2+lg5)+(lg2)^2=2lg5+2lg2+2lg2lg5+(lg5)^2+(lg2)^2=2lg5+2lg2+[2lg2lg5+(lg5)^2+(lg2)^2]=2lg(2*5)+(lg2+lg5)^2=2+1=32=(log2 5+1/2log2 0.2)(log5 2+1/2log5 0.5)=[log2 5+1/2(log2 2-log2 ...