Question

Решить,! завтра уже нужно сдать! заранее ! 1)3^x< 5^x 2)6^x> =2^x 3)(12/13)^x< =12^x 4)4^x*(3/8)^x< =2.25 5)5^x*(2/15)^x> =4/9 6)9^x*(1/18)^x> 0.25 7)3^x*(1/12)^x< 0.0625

Answer 1

$1)\; 3^{x}\ \textless \ 5^{x}\; ,\; (\frac{3}{5})^{x}\ \textless \ 1\; ,\; (\frac{3}{5})^{x}\ \textless \ (\frac{3}{5})^0\; \to \; x\ \textgreater \ 0\\\\2)\; 6^{x} \geq 2^{x}\; ,\; 3^{x} \geq 1\; ,\; 3^{x} \geq 3^0\to \; x \geq 0\\\\3)(\frac{12}{13})^{x} \leq 12^{x}\; ,\; (\frac{1}{13})^{x} \leq 1\; \to \; x \geq 0$

$4)\; 4^{x}\cdot (\frac{3}{8})^{x} \leq 2,25\\\\(\frac{3}{2})^{x} \leq \frac{9}{4}\; ,\; (\frac{3}{2})^{x} \leq (\frac{3}{2})^2\; \to \; x \leq 2\\\\5)\; 5^{x}\cdot (\frac{2}{15})^{x} \geq \frac{4}{9}\\\\(\frac{2}{3})^{x} \geq (\frac{2}{3})^2\; \to \; x \leq 2$

$6)\; 9^{x}\cdot (\frac{1}{18})^{x}\ \textgreater \ 0,25\\\\(\frac{1}{2})^{x}\ \textgreater \ \frac{1}{4}\; ,\; (\frac{1}{2})^{x}\ \textgreater \ (\frac{1}{2})^2\; \to \; x\ \textless \ 2\\\\7)\; 3^{x}\cdot (\frac{1}{12})^{x}\ \textless \ 0,0625\\\\(\frac{1}{4})^{x}\ \textless \ (\frac{1}{4})^2\; \to \; x\ \textgreater \ 2\\\\oo$