丨2^x-1-log3(x-1)丨不等式求X取值范围若丨2^x-1-log3(x-1)丨

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 01:22:37

丨2^x-1-log3(x-1)丨不等式求X取值范围若丨2^x-1-log3(x-1)丨
丨2^x-1-log3(x-1)丨不等式求X取值范围
若丨2^x-1-log3(x-1)丨<丨2^x-1丨+丨log3(x-1)丨则X的取值范围是?

丨2^x-1-log3(x-1)丨不等式求X取值范围若丨2^x-1-log3(x-1)丨
|a+b|<=|a|+|b|,当a,b同号或为0时取等于,即a*b>=0时取等
故丨2^x-1-log3(x-1)丨<丨2^x-1丨+丨log3(x-1)丨时
(2^x-1)(log3(x-1))<0
此时对x分段判断即可

∵丨2^x-1-log3(x-1)丨<丨2^x-1丨+丨log3(x-1)丨
∴2^x-1与 log3(x-1)同号

4/3>x>1
|a-b|<|a|+|b|
a b异号

(2^x-1)log3(x-1)>0
x>2