Question

Решите неравенства на приложенном скриншоте:

Answer 1

$7)\ \ 3^{3x-4}\leq 27\ \ ,\ \ \ 3^{3x-4}\leq 3^3\ \ \ \Rightarrow \ \ \ \ 3x-4\leq 3\ \ ,\\\\3x\leq 7\ \ ,\ \ x\leq \frac{7}{3}\ \ ,\ \ x\leq 2\frac{1}{3}\\\\x\in (-\infty ;2\frac{1}{3}\ ]$

$8)\ \ log_{1/2}(2x-2)\leq log_{1/2}x\ \ ,\ \ \ ODZ:\ \left\{\begin{array}{l}2x-2>0\\x>0\end{array}\right\ \left\{\begin{array}{ccc}x>1\\x>0\end{array}\right\ \ x>1\\\\0<\dfrac{1}{2}<1\ \ \ \to\ \ \ 2x-2\geq x\ \ ,\ \ \ x\geq 2\\\\x\in [\ 2\, ;\, +\infty \, )$

$9)\ \ log_3(x^2+6)<log_3\, 5x\ \ ,\ \ \ ODZ:\ x>0\\\\a=3>1\ \ \ \to \ \ \ x^2+6<5x\ \ ,\ \ \ x^2-5x+6<0\ \ ,\\\\x_1=2\ ,\ x_2=3\ \ (teorema\ Vieta)\\\\(x-2)(x-3)<0\ \ \ \ \ \ +++(2)---(3)+++\\\\x\in (\, 2\, ;\, 3\, )$