Question

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)

Answer 1

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
=3

2
=(log2 5+1/2log2 0.2)(log5 2+1/2log5 0.5)
=[log2 5+1/2(log2 2-log2 10)][log5 2+1/2(log5 5-log5 10)]
=(log2 5+1/2-1/2log2 10)(log5 2+1/2-1/2log5 10)
=[1/2log2 5+1/2+1/2log2(5/10)][1/2log5 2+1/2+1/2log2(2/10)]
=(1/2log2 5+1/2-1/2)(1/2log5 2+1/2-1/2)
=1/2log2 5*1/2log5 2
=1/4

就采纳我吧 我打的很不容易

Answer 2