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evgeniya97tjule
@evgeniya97tjule
July 2022
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Найдите наименьшее целое х, удовлетворяющее неравенству lg5^4x-lg2 5 > lg5^3x+3 + lg5
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sedinalana
Lg5^(4x)-lg25>lg5^(3x+3)+lg5
4x*lg5-2lg5>(3x+3)lg5+lg5
4x*lg5-2lg5-(3x+3)lg5-lg5>0
lg5*(4x-2-3x-3-1)>0
lg5(x-6)>0
lg5>0⇒x-6>0⇒x>6
x∈(6;∞)
Ответ наименьшее целое х=7
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Answers & Comments
4x*lg5-2lg5>(3x+3)lg5+lg5
4x*lg5-2lg5-(3x+3)lg5-lg5>0
lg5*(4x-2-3x-3-1)>0
lg5(x-6)>0
lg5>0⇒x-6>0⇒x>6
x∈(6;∞)
Ответ наименьшее целое х=7