[barisser]

Log is often used because it makes linear proportional returns. It makes the most sense when gains are considered derived from the principal, ie proportional returns from capital. See an example below.

As others have mentioned, maximizing log is equivalent to maximizing the underlying.

But when considering returns on accruing capital, a 20% loss is much worse than a 20% gain is good, and similarly a 100% gain is much less good than a 100% loss is bad. This is correctly captured by taking the log. In the case where money is simply accrued from some external source, and their is no proportional return, log isn't necessary.