What happens if you apply the "logarithm of a product" property to a negative number?

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We know that $\log_a xy=\log_a x + \log_a y$ and that logarithms of negative numbers are undefined. But what happens if we try to apply this property to let's say $-5$?

$\log_a-1*5=\log_a-1+\log_a5$

After that we can infinitely apply the same property, but where do we actually get the undefined part?