对数计算题
(log4_3+log2_3)(log3_2+log9_4) =(log4_3+log4_9)(log3_2+log3_2) =(log4_27)*(log3_4) =3(log4_3)*(log3_4) =3
设log2_3=x log4_3=x/2,log3_2=1/x,log9_4=log3_2=1/x 原式=3x/2*2/x=3
原式=[(lg3/lg4)+(lg3/lg2)][(lg2/lg3)+(lg4/lg9)](换底) =lg2/(2lg2)+lg3/(2lg3)+(lg3·lg2)/(lg2·lg3)+[lg3· (2lg2)]/[lg2·(3lg3)](展开) =1/2+1/2+1+2/3=8/3
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