Question

log1/3(5x-9)>=log1/3 4x​

Answer 1

$\displaystyle\bf\\ODZ:\\\\\left \{ {{5x-9 > 0} \atop {4x > 0}} \right. \ \ \ \Rightarrow \ \ \ \left \{ {{x > 1,8} \atop {x > 0}} \right. \ \ \ \Rightarrow \ \ \ x > 1,8\\\\\\\log_{\frac{1}{3} } \Big(5x-9\Big)\geq \log\Big(4x\Big)\\\\\\0 < \frac{1}{3} < 1 \ \ \ \Rightarrow \ \ \ 5x-9\leq 4x\\\\\\5x-4x\leq 9\\\\\\x\leq 9\\\\\\Otvet \ : \ x\in\Big(1,8 \ ; \ 9\Big]$