Question

Salut, aveti o idee la problema 31...?Mie mi-a dat raspunsul:

$x\geq \sqrt[3]{3}$

Answer 1

$\log_{\frac{1}{3}}(\log_{3}x)\geq 1 \\ \\ \log_{\frac{1}{3}}(\log_{3}x)\geq \log_{\frac{1}{3}}\frac{1}{3}\quad (\text{baza este }< 1\text{ se schimba semnul}) \\ \\ \log_3 x \leq \frac{1}{3} \\ \\ x\leq 3^{\frac{1}{3}} \\ \\ x \leq \sqrt[3]{3}\\ \\ \text{Dar x }> 1\\ \\ \Rightarrow x\in (1,\sqrt[3]{3}]$