To solve this equation, we can start by simplifying both sides using the properties of exponents.

On the left side, we have 3^-2.3^4.3^x. We can rewrite this as (3^(-2))(3^4)(3^x) using the product of powers property.

So, the equation becomes (3^(-2))(3^4)(3^x) = 3^7.

Now, we can simplify further by using the property of exponents that states: a^m * a^n = a^(m+n).

Therefore, we can rewrite the equation as 3^(-2 + 4 + x) = 3^7.

Simplifying the exponents on the left side, we have 3^(2 + x) = 3^7.

Since the bases are the same (3), we can equate the exponents:

2 + x = 7.

Solving for x, we subtract 2 from both sides:

x = 7 - 2.

Therefore, x = 5.