Question

8 и 7 задание с фотографии

Answer 1

$7)\; \; 4^{x+1}+7\cdot 2^{x}-2=0\\\\4^{x}\cdot 4+7\cdot 2^{x}-2=0\\\\4\cdot (2^{x})^2+7\cdot 2^{x}-2=0\\\\t=2^{x}\ \textgreater \ 0\; \; ,\; \; 4t^2+7t-2=0\\\\D=81\; ,\; \; t_1=\frac{-7-9}{8}=-2\ \textless \ 0\; ,\; t_2=\frac{1}{4}\ \textgreater \ 0\\\\2^{x}=\frac{1}{4}\; ,\; \; 2^{x}=2^{-2}\\\\x=-2$

$8)\; \; log_{0,1}(x-5)+log_{0,1}(x-2) \geq 1\; ,\; \; ODZ:\; x\ \textgreater \ 5\\\\log_{0,1}\Big ((x-5)(x-2)\Big ) \geq log_{0,1}0,1\\\\(x-5)(x-2) \leq 0,1\\\\x^2-7x+10 \leq 0,1\\\\x^2-7x+9,9 \leq 0\\\\D=9,4\; \; ,\; \; x_{1,2}= \frac{7\pm \sqrt{9,4}}{2} \\\\x_1\approx 1,97\; \; ,\; \; x_2\approx 5,03\\\\x\in (\, 5; \frac{7+\sqrt{9,4}}{2} \, ]$