Since you're asking where to use them, I feel a quick recap on what they
do is in order:
You're probably well familiar with the concept of raising a number exponentially. You take two numbers, a base and an exponent, and you raise the former by the latter (by multiplying the base by itself the number of times the exponent specifies) to get a power. For example, 2 (base) ^ 8 (exponent) = 256 (power).
With logarithms you're going the other way - you've already got the power and the base, but you want to figure out the exponent. For example, when you solve the power 10,000 using log base 10 you get the exponent of 4, because 10 to the 4 is 10,000.
One handy-dandy use for logarithms (which you're more likely to use than any other) is to figure out the root of a given number… but since that's such a common operation, most languages offer a specific function which does it for you.
In ComputerCraft, the only time I've even
considered using logs directly is to resolve the exponents of
colour values, though I quickly discarded the idea in favour of building a dedicated lookup table for the purpose. Logs're slow.
As ever,
Stack Overflow has a lot of great info. The example re the interest calculator strikes me as a fun project if you're looking for an excuse to try them out.
