To solve this equation, we need to isolate the variable x.

First, rewrite the equation as:

2^(3x-1) * 7^(3x-1) = 196

Next, rewrite 196 as a product of prime factors:

196 = 2^2 * 7^2

Now, substitute 196 with its prime factorization in the equation:

2^(3x-1) 7^(3x-1) = 2^2 7^2

Since the bases on both sides are the same, we can equate the exponents:

3x - 1 = 2
3x - 1 = 2

Solve for x:

3x = 2 + 1
3x = 3
x = 1

Therefore, the solution to the equation is x = 1.