各项都为正的等比数列An 若A5*A6=9 则LOg3a1+LOga2+LOga3+...+LOga10得多少啊

题目

各项都为正的等比数列An 若A5*A6=9 则LOg3a1+LOga2+LOga3+...+LOga10得多少啊
要具体点啊 LOg3a1+LOg3a2+LOg3a3+...+LOg3a10]=LOg3[a1*a2*a3.*a10]么

答案

Log3a1+Lo3ga2+Log3a3+...+Log3a10=Log3(a1*a2*a3.*a10)=Log3(a1*a10*a2*a9*.a5*a6)
=Log3((a5*a6)^5)
=5Log3(a5*a6)
=5Log3(9)
=10