Помогите решить неравенство [tex]2 log_{4}( {x}^{2} ) + log_{2}(x + 14) \leqslant - log_{ \frac{1}{2} }(x + 4) + 2 log_{2}(x + 2) [/tex]. Created by kuleshomaria. geometriya-ru

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July 2022 1 6 Report

Помогите решить неравенство
[tex]2 log_{4}( {x}^{2} ) + log_{2}(x + 14) \leqslant - log_{ \frac{1}{2} }(x + 4) + 2 log_{2}(x + 2) [/tex]

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Mihail001192

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Решено при помощи использования свойств логарифмов и метода интервалов:

$log_{ {a}^{n} }(b) = \frac{1}{n} log_{a}(b) \\ \\ log_{a}( {b}^{n} ) = n log_{a}(b) \\ \\ log_{a}(b) + log_{a}(c) = log_{a}(b \times c) \\$

ОТВЕТ: [ - 2/3 ; 0 ) U ( 0 ; 4 ]

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