To solve the equation 3^x + 3^x + 2 = 810, we can combine the like terms on the left side:

2 * 3^x + 2 = 810

Next, we can subtract 2 from both sides of the equation:

2 * 3^x = 808

Now, we can divide both sides of the equation by 2:

3^x = 404

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

ln(3^x) = ln(404)

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

x * ln(3) = ln(404)

Now, we can divide both sides of the equation by ln(3):

x = ln(404) / ln(3)

Using a calculator, we can find that ln(404) ≈ 5.9989 and ln(3) ≈ 1.0986. Therefore:

x ≈ 5.9989 / 1.0986 ≈ 5.46

So, the approximate value of x is 5.46.