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

Level pending

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?

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