指数函数中同指数不同底数的怎么比较大小

2025-03-15 13:52:52
推荐回答(2个)
回答1:

注意课本中指数函数的性质:
a>1时,指数大的函数值大,即
a>1时,x>y,则a^x>a^y;
0
1,3<5,所以
2^3<2^5
0.7^3与0.7^8,
底数=0.7,
0<0.7<1,
3<8,
所以
0.7^3>0.7^8.

回答2:

刚教给学生的方法:
一、若底数相同,指数不同,用指数函数的单调性来做;
二、若指数相同,底数不同,画出两个函数的图像,比如判断0.7^(0.8)与0.6^(0.8).
先画出f(x)=0.7^x,g(x)=0.6^x的图像,观察当x=0.8的函数图像的高低,来判断函数值大小即可;
其实这个确实可以用幂函数(估计过几个星期就学到了)来做,来判断单调性(这个有时候有可能
要涉及到导数问题,高三选修内容)
三、指数不同,底数也不同,找中间量,通常为1.但不排除其他的,比如判读0.7^(0.8),0.8^0.7,与1判断,结果两者都比1小,所以选另外的中间量0.7^0.7来做的。

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