Question

Помогите решить уравнение!!!

Answer 1

$2\cdot (\frac{2}{3} )^{x-1} -4\cdot (\frac{3}{2})^{x}+1=0\\\\2\cdot (\frac{2}{3})^{x}\cdot (\frac{2}{3})^{-1}-4\cdot (\frac{2}{3})^{-x}+1=0\\\\t= (\frac{2}{3} )^{x} \ \textgreater \ 0\; ,\; \; \; \; 3\cdot t-4\cdot \frac{1}{t} +1=0\\\\ \frac{3t^2+t-4}{t}=0 \; ,\; \; t\ne 0\\\\3t^2+t-4=0\; ,\; \; D=49\; ,\\\\t_1=1\; ,\; t_2=-\frac{4}{3}\ \textless \ 0\; ne\; \; podxodit\\\\(\frac{2}{3})^{x}=1\; \; \; \to \; \; \; ( \frac{2}{3})^{x}=(\frac{2}{3} )^{0}\\\\x=0$