For nearly 50 years theorists believed that if solving a problem takes t steps, it should also need roughly t bits of memory: 100 steps - 100bits. To be exact t/log(t).
Ryan Williams found that any problem solvable in time t needs only about sqrt(t) bits of memory: a 100-step computation could be compressed and solved with something on the order of 10 bits.
log to what basis? 2 or e or 10 or...
Why do programmers have to be so sloppy?
Except in mathematics and physics, where it usually is base e.
Except sometimes in computer science, where it can be base 2.
But there are more of those weirdnesses: "ld" can be "log decimal", so base 10; or "logarithmus dualis", so base 2. Base 2 is also sometimes written as "lb" (log binary). You really need to know the conventions of the field/subfield to know which is which.
I usually see either base e or base 2 as the default. In which applications do people use both logarithms and base 10 as the default? I mean, especially these day. In the olden days of the slide ruler base 10 was probably more common.
Engineering. For example dB is defined in base 10.