已知{log2an}为等比数列,且满足log2a1+log2a2+...log2a12=12,则a6*a7=
问题描述:
已知{log2an}为等比数列,且满足log2a1+log2a2+...log2a12=12,则a6*a7=
答
log2a1+log2a2+...log2a12=12∴ log2 (a1*a2*.a12)=12,且a1,a2,.a12都是正数a1*a2*a3*.a12=2^12∵a1*a12=a2*a11=a3*a10=a4*a9=a5*a8=a6*a7∴ (a6*a7)^6=2^12∴ a6*a7=2^2=4