If $$\log_4m + \log_4n = \log_2(m + n)$$ where m and n are positive real numbers, then which of the following must be true?

A

$$\frac{1}{m} + \frac{1}{n} = 1$$

B

m = n

C

$$m^2 + n^2 = 1$$

D

$$\frac{1}{m} + \frac{1}{n} = 2$$

E

No values of m and n can satisfy the given equation