Решите неравенство:lg(3x-7)>lg(x+1) Ответ должен быть : (2 1/3:4). Created by Ziffa. algebra-ru

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Ziffa @Ziffa

July 2022 1 10 Report

Решите неравенство:lg(3x-7)>lg(x+1)
Ответ должен быть : (2 1/3:4)

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sedinalana

Verified answer

{3x-7>0⇒3x>7⇒x>2 1/3
{x+1>0⇒x>-1
{3x-7>x+1⇒3x-x>1+7⇒2x>8⇒x>4
x∈(4;∞)

skvrtttskvrttt

$lg(3x-7)\ \textgreater \ lg(x+1)\to\left\{{{\left\{{{3x-7\ \textgreater \ 0}\atop{x+1\ \textgreater \ 0}}\right}\atop{3x-7\ \textgreater \ x+1}}\right\to\left\{{{\left\{{{x\ \textgreater \ 2\frac{1}{3}}\atop{x\ \textgreater \ -1}}\right}\atop{2x\ \textgreater \ 8}}\right\to\left\{{{x\ \textgreater \ 2\frac{1}{3}}\atop{x\ \textgreater \ 4}}\right$

ответ: $x\in(4;+\infty)$

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Ziffa July 2022 | 0 Ответы

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