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Chikuliya
@Chikuliya
August 2022
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Помогите решить неравенство
Log1/4 |x-2|>-1
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Amaimoon
Log1/4 |x-2|>-1
ОДЗ: |x-2|>0 ; x>2 (2;+∞)
log₂^-2 |x-2|>-1
-1/2log₂ |x-2|>-1 | домножим на -1
1/2log₂ |x-2|<1 ; 1=log₂ 2
1/2log₂ |x-2|<log₂ 2
log₂ |x-2|^1/2<log₂ 2
√|x-2|<2 | возведем обе части в квадрат.
|x-2|<4
x-2<4 и x-2>-4
x<6 x>-2
(-2;6)
Общее решение: (2;6)
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Answers & Comments
ОДЗ: |x-2|>0 ; x>2 (2;+∞)
log₂^-2 |x-2|>-1
-1/2log₂ |x-2|>-1 | домножим на -1
1/2log₂ |x-2|<1 ; 1=log₂ 2
1/2log₂ |x-2|<log₂ 2
log₂ |x-2|^1/2<log₂ 2
√|x-2|<2 | возведем обе части в квадрат.
|x-2|<4
x-2<4 и x-2>-4
x<6 x>-2
(-2;6)
Общее решение: (2;6)