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kotuk2000
@kotuk2000
August 2022
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Логарифмы, решите, пожалуйста, подробно
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sedinalana
Verified answer
Б
ОДЗ x>0 U x≠1
Прологарифмируем по основанию 5
log(5)5√5/log(5)x-(log(5)√5/log(5)x)²>1,25
1,5/log(5)x-0,25/log²(5)x>1,25
log(5)x=a
3/2x-1/4x²-5/4>0
(6a-1-5a²)/4a²>0
(5a²-6a+1)/4a²<0
5a²-6a+1=0
D=36-20=16
a1=(6-4)/10=1/5
U a2=(6+4)/10=1
4a²=0⇒a=0
+ + _ +
-------------(0)----------------(1/5)-------------(1)----------------
1/5<a<1⇒1/5<log(5)x<1⇒
x∈(
г
ОДЗ
(1-x)/(2-x)>0
x=1 x=2
x∈(-∞;1) U (2;∞)
(1-x)/(2-x)≤1/10
(1-x)/(2-x)-1/10≤0
(10-10x-2+x)/10(2-x)≤0
(8-9x)/(10(2-x)≤0
x=8/9 x=2
8/9≤x<2
x∈[8/9;1)
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Answers & Comments
Verified answer
БОДЗ x>0 U x≠1
Прологарифмируем по основанию 5
log(5)5√5/log(5)x-(log(5)√5/log(5)x)²>1,25
1,5/log(5)x-0,25/log²(5)x>1,25
log(5)x=a
3/2x-1/4x²-5/4>0
(6a-1-5a²)/4a²>0
(5a²-6a+1)/4a²<0
5a²-6a+1=0
D=36-20=16
a1=(6-4)/10=1/5
U a2=(6+4)/10=1
4a²=0⇒a=0
+ + _ +
-------------(0)----------------(1/5)-------------(1)----------------
1/5<a<1⇒1/5<log(5)x<1⇒
x∈(
г
ОДЗ
(1-x)/(2-x)>0
x=1 x=2
x∈(-∞;1) U (2;∞)
(1-x)/(2-x)≤1/10
(1-x)/(2-x)-1/10≤0
(10-10x-2+x)/10(2-x)≤0
(8-9x)/(10(2-x)≤0
x=8/9 x=2
8/9≤x<2
x∈[8/9;1)