Question

7^(x-2)>3^(2-x) решите неравенство

Answer 1

Ответ:

Пошаговое объяснение:

7^(x-2)>3^(2-x)

$\bf7^{x-2}>3^{2-x}\\\\\dfrac{7^x}{7^2} >\dfrac{3^2}{3^x}\\\\ \dfrac{7^x}{7^2} -\dfrac{3^2}{3^x}>0\\\\\dfrac{7^x\cdot3^x-49\cdot9}{49\cdot3^x} >0\\\\21^x>441\\\\21^x>21^2\\\\x>2\\\\Otvet:x\in(2;+\infty)$

Answer 2

$7^{x-2}>3^{2-x}$

$7^{x-2}>3^{-(x-2)}$

$7^{x-2}>\frac{1}{3^{x-2}}$   $|*3^{x-2}$

$7^{x-2}*3^{x-2}>1$

$21^{x-2}>1$

$21^{x-2}>21^0$

$x-2>0$

$x>2$

Ответ: х∈(2; +∞)