Is there a way to simplify $a\log(b) +\log(c)$?

Question

Very simply: $$a\log(b) +\log(c)$$

The coefficient on the first term is throwing me off.

Answer 1

Recall the properties $$a \log b = \log b^a$$ and $$\log a +\log b = \log ab.$$ Thus $$a\log b +\log c = \log b^a+\log c = \log(b^ac).$$

Answer 2

You can write $a\log(b) +\log(c)=\log(b^ac).$ Past that, there's not a lot we can do.