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Rauau1999
@Rauau1999
June 2022
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Решить уравнение(подробно)
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okneret
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Прологарифмируем по основанию 10
2lgx*lgx-lg10x=0
2lg²x-lgx-1=0
lgx=a
2a²-a-1=0
D=1+8=9
a1=(1-3)/4=-1/2⇒lgx=-1/2⇒x=1/√10
a2=(1+3)/4=1⇒lgx=1⇒x=10
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Answers & Comments
Verified answer
Прологарифмируем по основанию 102lgx*lgx-lg10x=0
2lg²x-lgx-1=0
lgx=a
2a²-a-1=0
D=1+8=9
a1=(1-3)/4=-1/2⇒lgx=-1/2⇒x=1/√10
a2=(1+3)/4=1⇒lgx=1⇒x=10