To solve this inequality, we need to find the range of possible values for x.

First, let's focus on the left inequality: 3^2 < 2^x.

3^2 = 9, so the inequality becomes 9 < 2^x.

Next, let's focus on the right inequality: 2^x < 128.

We can rewrite 128 as 2^7, so the inequality becomes 2^x < 2^7.

Now, we can combine the two inequalities:

9 < 2^x < 2^7.

To simplify this, we can take the logarithm base 2 of all three parts of the inequality:

log2(9) < log2(2^x) < log2(2^7).

Using the properties of logarithms, we can simplify further:

log2(9) < x < 7.

Therefore, the range of possible values for x is x > log2(9) and x < 7.

Approximating log2(9) to the nearest hundredth, we get:

x > 3.17 and x < 7.

So, the range of possible values for x is 3.17 < x < 7.