Решите уравнения: а)log5x=2log5(6-x)+1 б)log2(X-3)+3logx-3xчисла 4=5. Created by Сердцебеение. matematika-ru

Решите уравнения: а)log5x=2log5(6-x)+1 б)log2(X-3)+3logx-3xчисла 4=5...

Сердцебеение @Сердцебеение

July 2022 1 12 Report

Решите уравнения:
а)log5x=2log5(6-x)+1
б)log2(X-3)+3logx-3xчисла 4=5

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TARTILLO

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Решите уравнения:
а)log₅x=2log₅(6-x)+1 ОДЗ x>0 6-x>0 x∈(0;6)

log₅x=log₅(6-x)²+log₅5 log₅x=log₅5(6-x)² x=5(6-x)² 5x²-61x+180=0

x1=[61-√(61²-4·5·180)]/10 =[61-11]/10=5∈ОДЗ x2=[61+11]/10 =7,2∉ОДЗ

x=5

б)log₂(x-3)+3log(x-3x)числа 4=5
ПОЛАГАЮ ЧТО СКОРЕЕ ТАК...log2(X-3)+3log x-3 числа 4=5
ТОГДА ОДЗ: x>3 x-3≠1 x≠4
log₂(x-3)+3(log₂(x-3))/2=log₂32

2log₂(x-3)+3(log₂(x-3))=2log₂32

log₂(x-3)²+log₂(x-3)³=log₂32²

(x-3)²(x-3)³=32²
(x-3)⁵=(2⁵)² ⇔ x-3=4 x=7

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