若常数m>0,且m≠1,a,b,c成等比数列,则logma,logmb,logmc成等差数列
\u4e09\u4e2a\u6570\u6210\u7b49\u6bd4\u6570\u5217\uff0c\u82e5\u7b2c\u4e8c\u4e2a\u6570\u52a04\u5c31\u6210\u7b49\u5dee\u6570\u5217\uff0c\u518d\u628a\u8fd9\u4e2a\u7b49\u5dee\u6570\u5217\u7684\u7b2c3\u9879\u52a032\u53c8\u6210\u7b49\u6bd4\u6570\u5217\uff0c\u8fd9\u4e09\u4e2a\u6570\u662f\uff1f\u4e09\u4e2a\u6570\u6210\u7b49\u6bd4\u6570\u5217\uff0c\u8bbe\u4e3a\uff1aa,aq,aq^2
a,aq+4,aq^2\u6210\u7b49\u5dee\u6570\u5217\uff0c\u5f97\u5230\uff1a2(aq+4)=a+aq^2\u3002\u3002\u3002\u3002\u3002\u3002(1)
\u628a\u8fd9\u4e2a\u6570\u5217\u7684\u7b2c\u4e09\u9879\u52a032\u53c8\u6210\u7b49\u6bd4\u6570\u5217,\u5f97\u5230\uff1a
a,aq+4,aq^2+32\u6210\u7b49\u6bd4\u6570\u5217\uff0c\u5373:(aq+4)^2=a(aq^2+32)\u3002\u3002\u3002\u3002\u3002(2)
\u628a(2)\u5316\u7b80\uff0c\u5f97aq=4a-2.\u3002\u3002\u3002\u3002\u3002.(3)
\u4ee3\u5165\uff081\uff09,\u5f97\uff1a2(4a-2+4)=a+(4a-2)q
\u5373\uff1a2q=9a-12\u3002\u3002\u3002\u3002\u3002(4)
\u6d88q\uff0c\u5f97\uff1a
9a^2-20a+4=0
a=2\u62162/9
\u5f53a=2\u65f6\uff0c\u5f97q=3,\u6b64\u65f6\u8fd9\u4e09\u4e2a\u6570\u4e3a\uff1a2,6,18.
\u5f53a=2/9\u65f6\uff0c\u5f97q=-5,\u6b64\u65f6\u8fd9\u4e09\u4e2a\u6570\u4e3a\uff1a2/9,-10/9,50/9.
\u5e0c\u671b\u6211\u7684\u56de\u7b54\u80fd\u591f\u8ba9\u60a8\u6ee1\u610f
\u7528\u4ee3\u5165\u6cd5\u5c06\u5e26\u5165\u516c\u5dee-1\u7b49\u5dee\u6570\u5217\u4e3a\uff1a1 \uff0c0 \uff0c-1\uff0c
\u5c31\u662fa=0\uff0cb=-1\uff0c
\u518d\u628aa=0\uff0cb=-1\u4ee3\u5165\u7b49\u6bd4\u6570\u5217\u4e3a\uff1a3 \uff0c2\uff0c4
\u800c\u6570\u52173 \uff0c2\uff0c4\u4e0d\u662f\u7b49\u6bd4\u6570\u5217\uff0c\u6240\u4ee5\u5c31\u80fd\u6392\u9664\u7b49\u5dee\u6570\u5217\u516c\u5dee\u4e3a-1.
因为c-b=b-a=d
所以m^c/m^b=m^(c-b)=m^b/m^a=m^(b-a)=m^d
则logma,logmb,logmc成等差数列可以推出,a,b,c成等比数列
而a,b,c成等比数列推不出logma,logmb,logmc成等差数列
原因是，a、b、c如果是负数时情况
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