Question

Решите уравнение log3(x-1)=1-1log1/3(x-3)

Answer 1

$ODZ: \\ x \ \textgreater \ 0 \\ x \ \textgreater \ 3 \\ \\ log_3(x - 1) = 1 - log_{ \frac{1}{3}}(x - 3) \\ \\ log_3(x - 1) + log_{ \frac{1}{3}}(x - 3) = 1 \\ \\ log_3(x - 1) - log_3(x - 3) = 1 \\ \\ \dfrac{log_3(x - 1)}{log_3(x - 3)} = log_33 \\ \\ \dfrac{x - 1}{x - 3 } = 3 \\ \\ x - 1 = 3x - 9 \\ \\ 3x - x = -1 + 9 \\ \\ 2x = 8 \\ \\ x = 4 \\ \\ OTBET: \ x = 4.$