In the fifth day of Christmas, my true love sent to me 9 logarithms

Let $x$ be $471/2$ , $y$ be $43/2$ , and z be $4331/2$ .

The expression $\log_3(x + y) \times \log_5(y + z) \times \log_7(z + x) + \log_3(z + x) \times \log_5(x + y) \times \log_7(y + z) + \log_3(y + z) \times \log_5(z + x) \times \log_7(x + y) = \log_ab^c$

where $a,b,c \in R^+$

What is the value of a + b + c?