数列﹛An﹜是等比数列,且An＞0,﹙n∈N﹡﹚,a3a6a9＝4,则㏒2a2+㏒2a4＋㏒2a8+㏒2a10＝?因为a3a9=a6²,所以由a3a6a9=4,得a6³=4于是log₂a2+log₂a4+log₂a8+log₂a10=log₂[(a2a10)(a4a8)]=log̀

Question

数列﹛An﹜是等比数列,且An＞0,﹙n∈N﹡﹚,a3a6a9＝4,则㏒2a2+㏒2a4＋㏒2a8+㏒2a10＝?
因为a3a9=a6²,
所以 由a3a6a9=4,得a6³=4
于是log₂a2 +log₂a4 +log₂a8+log₂a10
=log₂[(a2a10)(a4a8)]
=log₂a6²a6²
=log₂a6⁴
=log₂4^(4/3)
=(4/3)log₂4
=8/3
问题：
=log₂a6⁴
=log₂4^(4/3)
请问下这个如果变成=log₂4^(4/3)的啊?这个

Answer 1

a3a6a9＝4
得a³6=4
∴a6=4^(1/3)
log₂（a6）⁴
=log₂[4^(1/3)]⁴
=log₂4^(4/3)
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