I know for a fact that it is not $\log x + \log y$, but Im unsure as to how to proceed.. I have checked the basic log properties but nowhere do they give an example of a statement like the one above.
Thanks in advance
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$\begingroup$There's no easy, or more or less generally useful, expansion of this thing. You could try though:
$$\log(x+y)=\log\left(x\left(1+\frac{y}{x}\right)\right)=\log x+\log\left(1+\frac{y}{x}\right)$$
The above is assuming $\,x>0\,$, and it doesn't look that nice or useful, does it? But who knows, perhaps under certain circumstances...
Of course, you can do the above factoring out $\,y\,$, too.
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