Question

Solution set of $x(2^x-1)(3^x-9)(x-3)<0$ is

• A. $(2,3)$
• B. $(-\infty ,0)\cup (2,3)$
• C. $(-\infty ,2)\cup (3,\infty )$
• D. $(-\infty ,0]\cup [3,\infty )$

Answer 1

The correct option is A $(2,3)$

Critical points are $0,2$ and $3.$
Here, critical point $0$ has even $\left(2\right)$ powers. That’s why sign doesn’t change at $x=0.$
$\therefore x\in (2,3)$