log1/3(log4(x^2-1))меньше и равно 1. Created by dashavishn. matematika-ru

3(log4(x^2-1))меньше и равно 1...

dashavishn @dashavishn

July 2022 2 10 Report

log1/3(log4(x^2-1))меньше и равно 1

платон14 Какой лог я не понял

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flsh $log_{ \frac{1}{3}}(log_{4}( x^{2} -1)) \leq 1$
ОДЗ: x² - 1 > 0 $log_{4}( x^{2} -1)$ >0
x < -1 и x > 1 x<-√2 и x>√2
Окончательно, ОДЗ: x<-√2 и x>√2
$log_{ \frac{1}{3}}(log_{4}( x^{2} -1)) \leq log_{ \frac{1}{3}}\frac{1}{3}$
$log_{4}( x^{2} -1) \geq \frac{1}{3}$
$x^{2} -1 \geq 4^\frac{1}{3}$
$x^{2}\geq 1+4^\frac{1}{3}$
x $\leq -\sqrt{1+4^\frac{1}{3}}$ и х $\geq \sqrt{1+4^\frac{1}{3}}$

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