Find all values of the parameter a for which the inequality `a.9^x +4(a-1)3^x+a gt 1` is satisfied for all real values of x

Explanation

To solve the inequality \( a \cdot 9^x + 4(a-1) \cdot 3^x + a > 1 \) for all real values of \( x \), we can follow these steps:

### Step 1: Rewrite the Inequality
We start with the given inequality:
\[ a \cdot 9^x + 4(a-1) \cdot 3^x + a > 1 \]
We can express \( 9^x \) as \( (3^x)^2 \):
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