Question

помогите решить уравнение

Answer 1

$(frac{1}{3})^{5x-1}-(frac{1}{3})^{5x}=frac{4}{9}\\(frac{1}{3})^{5x}:frac{1}{3}-(frac{1}{3})^{5x}=frac{4}{9}\\3(frac{1}{3})^{5x}-(frac{1}{3})^{5x}=frac{4}{9}\\2(frac{1}{3})^{5x}=frac{4}{9}|:2\\(frac{1}{3})^{5x}=frac{2}{9}.\\ 5x=log_{1/3}(2/9)\\ 5x=-(log_32-log_39)\\5x=-log_32+2\\x=-frac{1}{5} log_32+frac{2}{5}.$

ОТВЕТ: {$-frac{1}{5} log_32+frac{2}{5}$}.