MathBench > Measurement

Logs and pH

Special Cases

We know that

log(1000) = 3, and

log (0.001) = -3

What about a number that has both a "large" part before the decimal and a "small" part after the decimal? Such as...

log(1000.001) = ???

Remember, the whole purpose of logs is to tell you approximately how big the number is. Therefore, the decimal part (0.001) is really pretty unimportant compared to the whole-number part (1000). So, the log of this number is pretty close to the log of 1000, plus a tiny bit thrown in for the 0.001. In fact, with the help of google, I can find out that

log(1000.001) = 3.00000043

Okay, one more special case...

Somebody out there is asking, what about negative numbers? Where do they fit into all of this???

the answer is, log(1) = 0

Well, the short answer is, they don't. Negative numbers are the left out in the cold when it comes to logs. They just don't get no respect.

Which is generally ok. Usually we are using logs because we want to compare the amount of something we counted ... and that's usually a positive number, otherwise we couldn't count it.

Sometimes it does cause problems (especially in statistics), so people who use logs alot have ways to get around those problems, but we won't discuss that here. For our purposes, just remember you can't take the log of a negative number, even if you do feel sorry for it.