СРОЧНО!!! 40 БАЛЛОВ СРОЧНО!!! 40 БАЛЛОВ. Created by vikatrvka. algebra-ru

СРОЧНО!!! 40 БАЛЛОВ СРОЧНО!!! 40 БАЛЛОВ...

vikatrvka @vikatrvka

August 2022 1 29 Report

СРОЧНО!!! 40 БАЛЛОВ СРОЧНО!!! 40 БАЛЛОВ

Answers & Comments

Fire1ce

Verified answer

Ответ:

1) Г - x=(-1); 2) Б - х=±2; 3) 4 - (-∞;-1).

Пошаговое объяснение:

Свойства логарифмов:

$\Large \boldsymbol {} \text{ $ \boldsymbol{\sf \star \ c^x=a\Longrightarrow x=\log_{c}{a},\ a > 0,\ a\neq 1,\ b > 0 }$ \boldsymbol} \\\\ \text{ $ \boldsymbol{\sf \star \ \log_{c}{a^k}=k*\log_{c}{a} ,\ a > 0,\ c > 0, c\neq 1,\ k\in\mathbb R }$ \boldsymbol} \\\\ \text{ $ \boldsymbol{\sf \star \ \log_{a}{a}=1,\ a > 0,\ a\neq 1}$ \boldsymbol}$

$\Large \boldsymbol {} 1. \left(\frac{3}{7}\right)^x= \frac{7}{3} \\\\x=\log_{\frac{7}{3} }{\frac{3}{7} }\\\\x=\log_{\frac{7}{3} }{ \left(\frac{7}{3}\right)^{-1} }\\\\x=-1 *\log_{\frac{7}{3} }{ \left(\frac{7}{3}\right) }\\\\x=-1*1\\\\x=-1$

1) Г - x=(-1)

$\Large \boldsymbol {} 2.\ 5^{x^2-2}=25\\\\ \log_{5}{25}=x^2-2\\\\\log_{5}{5^2}=x^2-2\\\\2*\log_{5}{5}=x^2-2\\\\x^2-2=2*1\\\\x^2=2+2\\\\x=\pm\sqrt{4}\\\\x=\pm2$

2) Б - х=±2.

$\Large \boldsymbol {} 3.\ 25*5^x-5^{2x+3} > 0\\\\5^2*5^x > 5^{2x+3}\\\\5^{2+x} > 5^{2x+3}\\\\2+x > 2x+3\\\\x-2x > 3-2\\\\-x > 1\\\\x < -1$

3) 4 - (-∞;-1).

1 votes Thanks 3

Answers & Comments

Verified answer

Ответ:

Пошаговое объяснение:

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