To solve the equation 5^x + 5^x = 650, we can combine the like terms on the left side of the equation:

2 * 5^x = 650

Next, we can divide both sides of the equation by 2 to isolate the term 5^x:

5^x = 650 / 2

Simplifying the right side of the equation:

5^x = 325

To solve for x, we can take the logarithm of both sides of the equation. Let's use the natural logarithm (ln):

ln(5^x) = ln(325)

Using the logarithmic property, we can bring down the exponent:

x * ln(5) = ln(325)

Now, we can divide both sides of the equation by ln(5) to solve for x:

x = ln(325) / ln(5)

Using a calculator, we can find the approximate value of x:

x ≈ 3.357