I gave several examples in my comment, but here's another with explicitly calculated logs:

1) $100 with certainty. Log base 10 is 2. So expected log wealth 2, expected wealth $100.

2) 50% chance of $1, for a log of 0. 50% chance of $1,000 with a log of 3. Expected log wealth is therefore ((0+3)/2)=1.5, and expected wealth is ($1+$1000)/2=$500.5.

1) has higher expected log wealth, but 2) has higher expected wealth.