Question

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

• A. $(\frac{8}{5},\infty )$
• B. $(\frac{4}{5},\frac{8}{5})$
• C. $(-\infty ,0)\cup (\frac{8}{5},\infty )$
• D. none of these

Answer 1

The correct option is C $(-\infty ,0)\cup (\frac{8}{5},\infty )$

We have
${\log }_2|4-5x|>2|4-5x|>0\Rightarrow x\in R-\left\{\frac{4}{5}\right\}$

Now
${\log }_2|4-5x|>2$
$\Rightarrow |4-5x|>2^2\left(\text{if base is greater than 1 then inequality remains same}\right)$
$\Rightarrow |4-5x|>4$
$\Rightarrow 4-5x<-4\text{or}4-5x>4$
$\Rightarrow x>\frac{8}{5}\text{or}x<0\therefore x\in (-\infty ,0)\cup (\frac{8}{5},\infty )$