等比数列{an}各项均为正数且a4*a7+a5*a6=16,log2a1+log2a2+...+log2a10=?
问题描述：
等比数列{an}各项均为正数且a4*a7+a5*a6=16,log2a1+log2a2+...+log2a10=?
答
a(n)=aq^(n-1),a>0,q>0.16 = a(4)*a(7)+a(5)*a(6)=a^2*q^9 + a^2*q^(9) = 2a^2q^9,a^2q^9 = 8.log_{2}a(1)+log_{2}a(2)+...+log_{2}a(10)=log_{2}[a(1)a(2)...a(10)]=log_{2}[a^(10)q^(1+2+...+9)]=log_{2}[a^(10)q^...