I have a distribution of travel time. I am looking to do a log with base 2 transformations to get better graphs. Since, log is undefined at 0, the function leaves out all these values.
Is there any way to preserve all values that have 0 travel time and just use log approximation on other values such that
if x >0 then log (x);
else 0

It's not sufficient to simply transform the data to log2. We would like to only modify the scales and x-ticks. But the underlying numbers are the same.

This example from the documentation seems most relevant. You can still read the graph and say "Lots of animals have a body weight around 10".