Solve `x(2^x-1)(3^x-9)^5(x-3)<0.`

Explanation

Let `E=x(2^(x)-1)(3^(x)-9)^5(x-3) `
Here `2^(x)-1=0impliesx=0` and when `3^(x)-9=0impliesx=2`
Now mark `x = 0, 2` and 3 on 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 while crossing ` x = 0.`
The sign scheme of E is as follows:

From the figure, we have `E lt 0" for "x in (2,3)`.