Question

The solution set of ${\log }_2|4-5x|⟩2$ is

• A. $\left(-\infty ,0\right)\bigcup \left(\frac{8}{5,}\infty \right)$
• B. $\left(\frac{4}{5},\frac{7}{5}\right)$
• C. $\left(0,\infty \right)$
• D. $\left(-\infty ,0\right)\bigcup \left(\frac{13}{5},\infty \right)$

Answer 1

The correct option is A $\left(-\infty ,0\right)\bigcup \left(\frac{8}{5,}\infty \right)$

${\log }_2\left|4-5x\right|>2$

$\left|4-5x\right|>4$

$4-5x<-4$ $4-5x>4$

$5x>8$ $-x>0$

$x>8/5$ $x<0$

$x\in \left(-\infty ,0\right)\cup \left(\frac{8}{5},\infty \right)$