Question

设数列{an}是由正项组成的等比数列 且满足a8*a9=4则log4a1+log4a2+log4a3+...+log4a

Answer 1

答：

等比数列An>0

A8*A9=4

则：A1*(q^7)*A1*(q^8)=4

所以：(q^15)*(A1)^2=4

所以：

log4(A1)+log4(A2)+.+log4(A16)

=log4(A1*A2*A3*.*A16)

=log4 [ q^(1+2+..+15) *(A1)^16]

=log4 { q^[(1+15)*15/2] *(A1)^16 ]

=log4 [ (q^120)*(A1)^16 ]

=log4 [(q^15)*(A1)^2]^8

=8*log4(4)

=8