To solve this equation, we can use the formula for the sum of a geometric series:

S = a * (r^n - 1) / (r - 1)

In this case, the first term (a) is 3^(x+1), the common ratio (r) is 3, and the number of terms (n) is 100.

So, the sum of the series is:

S = 3^(x+1) * (3^100 - 1) / (3 - 1)

Now, let's simplify the right side of the equation:

3^100 - 3^2/2 = 3^100 - 9/2

Now, we can equate the two sides of the equation:

3^(x+1) * (3^100 - 1) / (3 - 1) = 3^100 - 9/2

To simplify the equation further, we can cancel out the common factor of 3^100 - 1 on both sides:

3^(x+1) = (3^100 - 9/2) * (3 - 1) / (3^100 - 1)

Now, we can simplify the right side of the equation:

3^(x+1) = (3^100 - 9/2) * 2 / (3^100 - 1)

Next, we can cancel out the common factor of 2 on the right side:

3^(x+1) = (3^100 - 9/2) / (3^100 - 1)

Finally, we can simplify the equation further:

3^(x+1) = (3^100 - 9/2) / (3^100 - 1)

Therefore, the equation is:

3^(x+1) = (3^100 - 9/2) / (3^100 - 1)