Question

Proszę o rozwiązanie zadania

Answer 1

Odpowiedź:

[tex]x\in(-7,+\infty)[/tex]

Szczegółowe wyjaśnienie:

[tex]\left(\frac{9}{16}\right)^{x-2}*\left(\frac{80}{27}\right)^{x-2} < \left(1\frac{2}{3}\right)^{2x+5}\\\\\left(\frac{9}{16}*\frac{80}{27}\right)^{x-2} < \left(1\frac{2}{3}\right)^{2x+5}\\\\\left(\frac{1}{1}*\frac{5}{3}\right)^{x-2} < \left(\frac{5}{3}\right)^{2x+5}\\\\\left(\frac{5}{3}\right)^{x-2} < \left(\frac{5}{3}\right)^{2x+5}\\\\\text{Poniewa\.z }\frac{5}{3} > 1\text{, to}\\\\x-2 < 2x+5\\\\x-2x < 5+2\\\\-x < 7\ |:(-1)\\\\x > -7\\\\x\in(-7,+\infty)[/tex]