Question

0" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%20log_%7B5%7D%20%28%7Bx%7D%5E%7B2%7D%20-%203%29%20%3E%200" title=" log_{5} ({x}^{2} - 3) > 0">
1) " class="latex-formula" id="TexFormula2" src="https://tex.z-dn.net/?f=%20log_%7B4%7D%285%20-%203x%29%20%3E%201%29%20" title=" log_{4}(5 - 3x) > 1) ">

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Answer 1

$1)x \in (-\infty; -2) \cup (2; +\infty)\\2)x < \frac{1}{3}\\3)x \in [-\sqrt2; \sqrt2]$

Пошаговое объяснение:

$\begin{matrix}1)log_5(x^2-3) 0\\x^2-3 1\\x^2 4\\x \in (-\infty; -2) \cup (2; +\infty)\end{matrix}$

$\begin{matrix}2)log_4(5-3x) 1\\5-3x4\\3x < 1\\x < \frac{1}{3}\end{matrix}$

$\begin{matrix}3)lg(x^2-1) \leqslant 0\\x^2-1 \leqslant 1\\x^2 \leqslant 2\\x \in [-\sqrt2; \sqrt2]\end{matrix}$