script> Тогда неравенство примет вид: $\quad 40t^2-21t+2\le0.$

$40t^2-21t+2=0 \quad \Leftrightarrow \quad \begin{cases} t=\frac{1}{8},\\ t=\frac{2}{5}. \end{cases}$ $40t^2-21t+2\le0 \quad \Leftrightarrow \quad (8t-1)(5t-2)\le0.$

Решим полученное неравенство методом интервалов:

$\frac{1}{8}\le t\le \frac{2}{5} \quad \Leftrightarrow \quad 2^{-3}\le 2^x \le 2^{\log_2 \frac{2}{5}} \quad \Leftrightarrow \quad -3\le x \le \log_2 \frac{2}{5}.$

Таким образом, решением исходного неравенства является: $\quad x\in[-3;\; \log_2 \tfrac{2}{5}].$

Ответ: $\quad \left[-3;\; \log_2 \frac{2}{5}\right].$

41:{"original_url":"https://storage.yandexcloud.net/egehub/public/358707/JLsjN2NUSu98GSCkjSVJ9Zg3fcBF0fLznIp2ShtG.png","small_url":"https://storage.yandexcloud.net/egehub/public/358707/conversions/JLsjN2NUSu98GSCkjSVJ9Zg3fcBF0fLznIp2ShtG-small.png","medium_url":"https://storage.yandexcloud.net/egehub/public/358707/conversions/JLsjN2NUSu98GSCkjSVJ9Zg3fcBF0fLznIp2ShtG-medium.png","big_url":"https://storage.yandexcloud.net/egehub/public/358707/conversions/JLsjN2NUSu98GSCkjSVJ9Zg3fcBF0fLznIp2ShtG-big.png"} 42:{"original_url":"https://storage.yandexcloud.net/egehub/public/358709/o9Sl0aesxDsUxhoAeZwWoafqgJ4OuzQ3rDiZejyn.png","small_url":"https://storage.yandexcloud.net/egehub/public/358709/conversions/o9Sl0aesxDsUxhoAeZwWoafqgJ4OuzQ3rDiZejyn-small.png","medium_url":"https://storage.yandexcloud.net/egehub/public/358709/conversions/o9Sl0aesxDsUxhoAeZwWoafqgJ4OuzQ3rDiZejyn-medium.png","big_url":"https://storage.

Задание №29388 ЕГЭ по Математике