To solve the equation 2^x+1 - 2x = 64, we can start by simplifying the equation.

First, let's rewrite 2^x+1 as 2 * 2^x. This is because 2^x+1 is equal to 2^x * 2^1, and 2^1 is simply 2.

So, the equation becomes 2 * 2^x - 2x = 64.

Next, let's simplify further by factoring out a 2 from the first term:

2(2^x - x) = 64.

Now, divide both sides of the equation by 2:

2^x - x = 32.

Now, let's solve for x. Unfortunately, there is no algebraic way to solve this equation directly. We will need to use numerical methods or approximation techniques to find the solution.

One common method is to use trial and error or a graphing calculator to estimate the value of x that satisfies the equation. By trying different values of x, we can find that x ≈ 5 is a solution to the equation.

Therefore, the approximate solution to the equation 2^x+1 - 2x = 64 is x ≈ 5.