指数式、对数式、幂式的大小比较
题型一临界值法比较大小
[典例1](1)(2024·天津高考)若a＝4.2-0.3，b＝4.20.3，c＝log4.20.2，则a，b，c的大小关系为()
A．abc B．bac
C．cab D．bca
(2)已知a＝log52，b＝1log0.10.7，c＝0.70.3，则a，b
A．acb B．abc
C．bca D．cab
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临界值法比较大小的关键是寻找合适的中间值，如常考虑a，b，c与特殊数字“0”“1”“12”的大小关系．
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1．(1)(2025·山西运城模拟)设a＝140.8，b＝log0.30.2，c＝log0.30.4，则a，b，
A．abc B．bac
C．cab D．bca
(2)已知a＝2log32，b＝2log5
A．abc B．bac
C．cba D．cab
题型二数形结合法比较大小
[典例2](多选)(2025·重庆巴蜀中学模拟)已知实数a，b，c满足：2a＝13b＝log2
A．bac B．abc
C．acb D．bca
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本例属于方程根问题，求解的关键是等价转化为相应函数图象的交点问题，如将问题转化为函数y＝2x,y＝13x，y＝log2x的图象与直线y＝t
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2．(2025·山西晋中模拟)若ea＝－lna，e－b＝lnb，e－c＝－lnc，则()
A．abc B．acb
C．bca D．bac
题型三利用指数、对数及幂的运算性质比较大小
[典例3](1)设a＝ln22，b＝ln33，c＝ln66，则
A．abc B．bca
C．bac D．cab
(2)已知a＝3log83，b＝－12log1316，c＝log43，则a
A．abc B．cab
C．bca D．bac
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