Question

log 2/3 (x) + log 3 (x) = 2
Решите пожалуйста.

Answer 1

$log_{\frac{2}{3}}x+log_3x=2\\\\\frac{log_3x}{log_3\frac{2}{3}}+log_3x=2\ /\cdot log_3\frac{2}{3}\\\\log_3x+log_3\frac{2}{3}\cdot log_3x=2log_3\frac{2}{3}\\\\log_3x(1+log_3\frac{2}{3})=log_3(\frac{2}{3})^2\\\\log_3x(log_33+log_3\frac{2}{3})=log_3\frac{4}{9}\\\\log_3x(log_3(3\cdot\frac{2}{3}))=log_3\frac{4}{9}\\\\log_3x\cdot log_32=log_3\frac{4}{9}\ /:log_32\\\\log_3x=\frac{log_3\frac{4}{9}}{log_32}\\\\log_3x=log_2\frac{4}{9}\\\\x=3^{log_2\frac{4}{9}}$