Note: I assume this is because log() returns a floating point value. I.e. it's a precision issue?

Floating point values have a limited precision. Hence a value might 
not have the same string representation after any processing. That also
includes writing a floating point value in your script and directly 
printing it without any mathematical operations.

If you would like to know more about "floats" and what IEEE
754 is, read this:
http://docs.sun.com/source/806-3568/ncg_goldberg.html
 
Thank you for your interest in PHP.

Try having a look at this:
echo serialize(log(1000, 10));

When you cast to int you just truncate the fractional part.

Exactly right: the first value is being rendered as 3 because of the fact that PHP limits the significant digits shown when converting a float to a string. If you look at the value of serialize(log(1000, 10)), you'll end up with something like the following:

d:2.999999999999999555910790149937383830547332763671875;

Which demonstrates that the internal representation is slightly less than 3. The explicit conversion to an integer causes the value to be rounded down, hence why you get 2.