Solve x(2^x-1)(3^x -9)(x-3)<0.

Let $E = x(2^x-1)(3^x-9)(x-3)$

Here $2^x-1=0⇒x=0$ and when $3^x-9=0⇒x=2$

Now mark x = 0, 2 and 3 or real number line.

The sign of E starts with a positive sign from right hand side.

Also at x = 0, two factors vanish x and $2^x-1$; hence, the sign of E does not change wile crossing x = 0.

The sign scheme of E is as follows:

From the figure, we have E < 0 for $x ∈ (2, 3)$