Proper syntax for summation of logarithms

Question

In my textbook I found:

$$\sum_{k=1}^{n}\ln{(k)}=\log(1)+\log(2)+\log(3)+\cdots+\log(n)$$ Shouldn't it be: $$=\ln(1)+\ln(2)+\ln(3)+\dotsb+\ln(n)\;\text?$$

Answer 1

Most likely it is a typo, as using different notation $\ln$ and $\log$ in the same expression is bad style in my view.

However, it is not incorrect. The default base for the logarithm depends on the context, and very often it will be $2, 10$ or $e$.

Answer 2

It's at least inconsistent, yes. That being said, in many textbooks $\log x$ actually means the natural logarithm.

Answer 3

As suggested above, it is not technically incorrect. You can always check the Errata (Google 'textbook name': Errata) - if one exists to see if this was an error.