Решите уравнение: [tex] log_5(x-1)+log_5(x-2)=log_5(x+2) [/tex]. Created by Narberall. matematika-ru

x∈(2,+∞) Используем :x=0 или x=4 x=0∉(2,+∞) Ответ: x=4

tex]...

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July 2022 1 9 Report

Решите уравнение:
[tex] log_5(x-1)+log_5(x-2)=log_5(x+2) [/tex]

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malakasha

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$log_{5}(x-1)+log_{5}(x-2)=log_{5}(x+2)$
x∈(2,+∞)
Используем : $log_a(x)+log_a(y)=log_a(x*y)$
$log_{5}((x-1)*(x-2)=log_{5}(x+2)$
$log_5(x^2-2x-x+2)=log_5(x+2)$
$x^2-2x-x+2=x+2$
$x^2-3x-x=0$
$x^2-4x=0$
$x*(x-4)=0$
x=0 или x=4
x=0∉(2,+∞)
Ответ: x=4

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Narberall July 2022 | 0 Ответы

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