# 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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