Question

Решите уравнение и неравенство

Answer 1

$1)\; \; \frac{x-3}{log_5x}\leq 0\; \; \; ,\; \; \; ODZ:\; x>0\; ,\; x\ne 1\\\\\left \{ {{x-3\geq 0} \atop {log_5x<0}} \right.\quad ili\quad \left \{ {{x-3\leq 0} \atop {log_5x>0}} \right.\\\\\left \{ {{x\geq 3} \atop {x<1}} \right.\qquad ili\qquad \left \{ {{x\leq 3} \atop {x>1}} \right.\\\\x\in \varnothing \qquad ili\qquad 1<x\leq 3\\\\Otvet:\; \; x\in (1,3\, ]\; .$

$2)\; \; \frac{6^{x^2}}{3^2}=\frac{2^2}{6^{8-5x}}\\\\6^{x^2}\cdot 6^{8-5x}=2^2\cdot 3^2\\\\6^{x^2-5x+8}=6^2\\\\x^2-5x+8=2\\\\x^2-5x+6=0\\\\x_1=2\; ,\; x_2=3\; \; \; (teorema\; Vieta)\\\\Oyvet:\; \; x_1=2\; ,\; x_2=3\; .$