求高一数学练习123的答案和解析 例题不用

练习一：(1)：2^(1-log2(3))
=2^1*2^(-log2(3))
=2*(1/3)
=2/3
(2)：log4(3)*log9(2)-log1/2(√32)^(1/4)
=lg3/lg4*lg2/lg9+1/4*log2(2^5)
=1/4+1/4*5
=3/2
练习二：lg5*log√10(20)+[lg2^(√2)]^2-3^(log3(2)-1)
=lg5*lg400+2*(lg2)^2-3^(log3(2))*3^(-1)
=lg5*(2lg5+4lg2)+2*(lg2)^2-2*(1/3)
=2*(lg5)^2+4lg2lg5+2*(lg2)^2-2/3
=2*(lg2+lg5)^2-2/3
=4/3
练习三：用log6(5)=a,log6(3)=b表示log75(12)
log75(12)=lg12/lg75=(lg6+lg2)/(2lg5+lg3)
log6(5)=lg5/lg6=a
log6(3)=lg3/lg6=b
∴(lg6+lg2)/(lg25+lg3)=[lg6+(lg6-lg3)]/(2lg5+lg3)
=(2lg6-blg6)/(2alg6+blg6)
=(2-b)/(2a+b)
点评：这几题主要考查换底公式的应用以及对数的基本运算，需加强练习，熟练掌握