To solve the equation 2^x + 10 = 37, we need to isolate the variable x.

First, subtract 10 from both sides of the equation:
2^x + 10 - 10 = 37 - 10
2^x = 27

Next, we can rewrite 27 as 3^3:
2^x = 3^3

Since the bases are different, we can take the logarithm of both sides of the equation to solve for x. Let's use the natural logarithm (ln) here:
ln(2^x) = ln(3^3)

Using the property of logarithms, we can bring down the exponent:
x ln(2) = 3 ln(3)

Finally, divide both sides of the equation by ln(2) to solve for x:
x = (3 ln(3)) / ln(2)

Using a calculator, we can approximate the value of x to be:
x ≈ 4.807