Question

数学速度来啊

Answer 1

(1)
lg1/4 - lg25=lg(1/4/25)=lg(1/100)=-2

(2)
=log₅10²+log₅0.25=log₅(10²*0.25)=log₅25=2

(3)
=2log₅5²-3log₂2⁶=2*2-3*6=4-18=-14

(4)
=log₂(log₂2⁴)=log₂4=2

(5)
=((log₂3)/2+(log₂3)/3)(log₃2+(log₃2)/2)
=(log₂3)(5/6)(log₃2)(3/2)
=(5/6)*(3/2)
=5/2/2
=5/4

Answer 2

Answer 3

1)原式=lg(1/4*1/25)=lg(1/100)=lg[10^(-2)]=-2
2)原式=log5(100*0.25)=log5(25)=log5(5^2)=2
3)原式=2*2log5(5)-3log2(2^6)=2*2-3*6=-14
4)原式=log2[log2(2^4)]=log2(4)=log2(2^2)=2
5)原式=[1/2log2(3)+1/3log2(3)][log3(2)+1/2log3(2)]
=5/6log2(3)*3/2log3(2)
=5/6*3/2[log2(3)*log3(2)]
=5/4*1
=5/4

Answer 4

(1)=-lg4-lg25=-lg100=-2
(2)=log5(10^2*0.25)=log5(25)=2
(3)=2*2-3*6=-14
(4)=log2(4)=2
(5)=(log4(3)+1/2log4(3))*(log3(2)+1/2log3(2))=3/2log4(3)*3/2log3(2)
=9/4*1/2log2(3)*log3(2)=9/8*1=9/8

Answer 5

1: -2 2: 2 3: -14 4: 2 5:10/9