在由正数组成的等比数列中,a4a5a6=3,log3(a1)+log3(a2)+log3(a8)+log3(a9)=

题目

在由正数组成的等比数列中,a4a5a6=3,log3(a1)+log3(a2)+log3(a8)+log3(a9)=

答案

a4a5a6=3,所以a5的立方=3 a1*a2*a8*a9=(a2*a8)*(a1*a9)=a5四次方log3(a1)+log3(a2)+log3(a8)+log3(a9) =log3(a1*a2*a8*a9) =log3(a1*a2*a8*a9) =log3(a5四次方) =log3(3的三分之四次方) =4/3