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

Explanation

To solve the inequality \( x(2^x - 1)(3^x - 9)^5(x - 3) < 0 \), we will follow these steps:

### Step 1: Identify the points where the expression equals zero.
We start by setting each factor in the expression to zero:

1. \( x = 0 \)
2. \( 2^x - 1 = 0 \) implies \( 2^x = 1 \) which gives \( x = 0 \).
3. \( 3^x - 9 = 0 \) implies \( 3^x = 9 \) which gives \( x = 2 \).
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