Question

Solution set of the inequality $lo{g}_7\frac{x-2}{x-3}<0$ is

• A. $(-\infty ,2)$
• B. $(2,\infty )$
• C. $(-\infty ,3)$
• D. $(3,\infty )$

Answer 1

The correct option is A

$(-\infty ,2)$

As the argument of a logarithm should be greater than zero
$\Rightarrow \frac{x-2}{x-3}>0$

$lo{g}_7\frac{x-2}{x-3}<0$
$\Rightarrow \frac{x-2}{x-3}<1$

$\Rightarrow \frac{x-2}{x-3}>0$ and $\frac{x-2}{x-3}-1<0$
$\Rightarrow x<2;x>3$ and $x<3$
The intersection of both solutions is
$\Rightarrow x<2$
Thus, solution set is $(-\infty ,2)$