The solution set of the system of equations log2x + log2y = log29 + 1,    is (p, q) then

Sure, let's solve the system of equations step by step.

Given equation is log2x + log2y = log29 + 1

Step 1: We know that loga + logb = log(ab). So, we can rewrite the equation as log2(xy) = log29 + 1

Step 2: We also know that loga^n = nloga. So, we can rewrite the equation as log2(xy) = log2(2^9) + log2(2)

Step 3: Simplifying the right side of the equation, we get log2(xy) = log2(512*2) = log2(1024)

Step 4: If loga = logb, then a = b. So, we can equate the arguments of the logarithms to get xy = 1024

Step 5: The problem doesn't specify any other relationship between x and y, so there are multiple solutions. For example, if x = 2 and y = 512, then xy = 1024. Similarly, if x = 32 and y = 32, then xy = 1024.

So, the solution set (p, q) could be any pair of positive numbers such that their product is 1024.