Question

预习作业！！！①loga2+loga1/2(a>0,且a≠1) ②log3(18)-log3(2) ③1g1/4-1g25

④ 2log5(10)+log5(0.25)
⑤2log5(25)-3log2(64)
⑥log2(log2(16) 过程 详细

Answer 1

①loga2+loga1/2=log(a)2+log(a)2^(-1)=log(a)2-log(a)2=0
②log3(18)-log3(2)=log(3)(2*9)-log(3)2=log(3)2+log(3)9-log3(2)=log(3)9=log(3)3^2=2log(3)3=2
③1g1/4-1g25=lg2^(-2)-lg5^2=-21g2-2lg5=-2*(lg2+lg5)=-2*lg(2*5)=-2lg10=-2
④ 2log5(10)+log5(0.25) =2log(5)(2*5)+log(5)(1/4)=2log(5)5+2log(5)2+log(5)1-log(5)4
=2log(5)5+2log(5)2+log(5)1-log(5)2^2=2+2log(5)2+0-2log(5)2=2
⑤2log5(25)-3log2(64)=2log(5)(5^2)-3log(2)(2^6)=4log(5)5-(3*6)log(2)2=4-18=-14
⑥log2(log2(16) =⑥log2(log(2)(2^4) )=⑥log2(4log(2)2)= log2(4)=log(2)(2^2)=2log(2)2=2

Answer 2

（1）loga2+loga1/2=loga2+loga2^-1=loga2-1xloga2=0
（2）log3(18)-log3(2)=log3（18÷2）=log3 9=2
（3）1g1/4-1g25=1g（1/4÷25）1g0.01=-2
（4）2log5(10)+log5(0.25)=log5(10)^2+log5(0.25)=log5（100乘0.25）=log5 25=2
（5）2log5(25)-3log2(64)=log5(25)^2-log2(64)^3=log5 5^4-log2 2^18=4-18=-14
（6）log2(log2(16)）=log2(log2(2^4））=log2 4=log2 2^2=2
最后说句 这些都是我自己算的 有错的地方多包涵啊~

Answer 3

对数运算法则知道不？