Question

Показательное неравенство

Answer 1

Ответ:

${2}^{x + 2} - {2}^{x + 3} - {2}^{x + 4} > {5}^{x + 1} - {5}^{x + 2} \\ {2}^{x + 2} (1 - 2 - {2}^{2} ) > {5}^{x + 1} (1 - 5) \\ {2}^{x + 2} \times ( - 5) > {5}^{x + 1} \times ( - 4) \\ {2}^{x + 2} \times 5 > {5}^{x + 1} \times 2 \times 2 \\ \frac{ {2}^{x + 2} }{2 \times {5}^{x + 1} } > \frac{2}{5} \\ \\ \frac{ {2}^{x + 1} }{ {5}^{x + 1} } > \frac{2}{5} \\ {( \frac{2}{5}) }^{x + 1} > \frac{2}{5} \\ x + 1 < 1 \\ x < 0$