设等比数列{an}中,每项均为正数,且a3*a8=81,log3(a1)+log3(a2)+…+log3(a10)等于?

题目

设等比数列{an}中,每项均为正数,且a3*a8=81,log3(a1)+log3(a2)+…+log3(a10)等于?

答案

a3*a8=81
a1*a10=a2*a9=a3*a8=……=a5*a6=81
log3(a1)+log3(a2)+…+log3(a10)
=log3(a1*a2*……*a10)
=log3[(a1*a10)*(a2*a9)……(a5*a6)]
=log3[(81)^5]
=5log3(81)
=5*4
=20