In the old days, when people used logarithm tables to do multiplication, the page after the log tables was the antilog tables (to base ten of course). You looked up the logs of your numbers, added them, and then looked up the antilog of that.
THESE tables aim at popularising logarithms. Like other four-figure tables they give the logarithms of numbers from 1000 to 9999. While the ordinary tables give these in one opening of two pages by ...
Logarithms are defined as the solutions to exponential equations and so are practically useful in any situation where one needs to solve such equations (such as finding how long it will take for a population to double or for a bank balance to reach a given value with compound interest). Historically, they were also useful because of the fact that the logarithm of a product is the sum of the ...
The discrete Logarithm is just reversing this question, just like we did with real numbers - but this time, with objects that aren't necessarily numbers. For example, if $ {a\cdot a = a^2 = b}$, then we can say for example $ {\log_ {a} (b)=2}$.
So in most applications, we refuse to use negative bases. HOWEVER, just because the concept of "logarithm" isn't a function on the complex plane, does not mean that we can't USE complex logarithms: it's just that we have to do something called a "branch cut", which basically picks one output for all values in a consistent way.
I would like to know how logarithms are calculated by computers. The GNU C library, for example, uses a call to the fyl2x() assembler instruction, which means that logarithms are calculated directl...