Question

8 и 7 задание с фотографии

Answer 1

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

$8); ; log_{0,1}(x-5)+log_{0,1}(x-2) geq 1; ,; ; ODZ:; x textgreater 5\\log_{0,1}Big ((x-5)(x-2)Big ) geq log_{0,1}0,1\\(x-5)(x-2) leq 0,1\\x^2-7x+10 leq 0,1\\x^2-7x+9,9 leq 0\\D=9,4; ; ,; ; x_{1,2}= frac{7pm sqrt{9,4}}{2} \\x_1approx 1,97; ; ,; ; x_2approx 5,03\\xin (, 5; frac{7+sqrt{9,4}}{2} , ]$