等差数列证明题

问题描述:

等差数列证明题
已知logaX,logbX,logcX成等差数列,且X不等于1,试证:1/lga,1/lgb,1/lgc成等差数列

logaX,logbX,logcX成等差数列
logcX-logbX=logbX-logaX
2logbX=logaX+logcX
两边同取以10为底的对数:
2lgx/lgb=lgx(1/lga+1/lgc)
2/lgb=1/lga+1/lgc
1/lgc-1/lgb=1/lgb-1/lga
1/lga,1/lgb,1/lgc成等差数列