Question

有关数列的的数学题等比数列{an}中,an>0,a5*a6=9,则log3a1+log3a2…+log3a10等于多少?

Answer 1

log3a1+log3a2…+log3a10=log3（a1*a2*a3*a4*a5*a6*a7*a8*a9*a10）

等比数列{an}中,an>0,有公式,若m+n=p+q,则am*an=ap*aq,

所以a1*a10=a2*a9=a3*a8=a4*a7=a5*a6=9,

所以a1*a2*a3*a4*a5*a6*a7*a8*a9*a10=9^5=3^10

故,log3a1+log3a2…+log3a10=log3（a1*a2*a3*a4*a5*a6*a7*a8*a9*a10）=10