To solve this equation, we can start by simplifying both sides:

2.5^(x+1) = 1000
6.5^2 = 42.25

Now, we can rewrite the equation as:

2.5^(x+1) = 42.25

Next, we can take the logarithm of both sides to eliminate the exponent:

log(2.5^(x+1)) = log(42.25)

Using the logarithmic property log(a^b) = b*log(a), we can rewrite the equation as:

(x+1) * log(2.5) = log(42.25)

Now, we can solve for x by isolating it:

x + 1 = log(42.25) / log(2.5)

Finally, we can solve for x:

x = (log(42.25) / log(2.5)) - 1

Using a calculator, we find that x ≈ 3.