My first thought is that logs are computed using the same concept, so it doesn't make it any faster or more accurate. However, it's always
log, with other things expressed in terms of log, so that function can be optomized.
Then I realized that real libraries use a Taylor/Macloren (spelling?) series to compute log and other functions, not Newton's method. This is code tuned to the specific function, and you can't do as well with an arbitrary input function unless you input the first derivitive as well.