an为等比数列,若a>0,log3a1+log3a2+...log3a10=20,求a5×a6
问题描述:
an为等比数列,若a>0,log3a1+log3a2+...log3a10=20,求a5×a6
答
an为等比数列,由等比中项得
a1*a11=a2*a9=a3*a8=...a5*a6
log3a1+log3a2+...log3a10=20
则log3(a5*a6)^5=5log3(a5*a6)=20
则log3(a5*a6)=4
所以a5*a6=3^4=81