To solve the equation 3^x + 25 = 26.2² + 2.3⁰, we can simplify the right side first.

26.2² = 26.2 * 26.2 = 686.44

2.3⁰ = 1 (any number raised to the power of 0 is equal to 1)

So, the equation becomes:

3^x + 25 = 686.44 + 1

3^x + 25 = 687.44

Now, subtract 25 from both sides:

3^x = 687.44 - 25

3^x = 662.44

To solve for x, we need to take the logarithm of both sides. Let's take the logarithm base 3:

log₃(3^x) = log₃(662.44)

x = log₃(662.44)

Using a calculator, we find that x ≈ 6.08.