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