You can learn more about it in our log base 2 calculators. There is also the binary logarithm, i.e., log with base 2, but it's not as common as the first two. We denote them ln(x) and log(x) (the second one simply without the small 10), and their bases are, respectively, the Euler number e and (surprise, surprise!) the number 10. There are two very special cases of the logarithm which have unique notation: the natural logarithm and the logarithm with base 10.For example:Īnd for those who prefer symbols instead of bunnies, here's the formal definition of a logarithm:īefore we expand the logarithmic expressions and see the formulas, let's mention a few essential facts concerning logs: However, as opposed to logarithms, roots return the exponent base, not the exponent itself (in the above language: they return the size of a single litter, not the number of generations that have to pass). Note that taking a root is also considered an inverse operation to taking a power. Observe that the little 6 corresponds to the size of a single litter.
Our animal example corresponds to wondering how many generations have to pass before we get a fixed number of little ones. The logarithm is the inverse operation to an exponent. Therefore, if each of a couple's kids got another 6 small ones later in life (with an outside partner, of course), and the same for their kids, and their kids, then we can calculate how big the fourth generation is with a new mathematical tool: exponents: Obviously, the next generation has similar interests to their parents. Therefore, if, for instance, we had 4 couples and each got 6 younglings, we describe the overall number of little ones using multiplication:
The meeting of two such animals (of the opposite sex, of course) leads to more rabbits. From the very moment two rabbits met each other and decided to prolong the existence of their species, all they had in mind was mathematics, even if they didn't quite know it.Īpart from raising the probability of their survival (which, as we know, was very successful), the rabbits managed to become a symbol of multiplication. Some of you may disagree, but deep down, we all know that mathematics lies at the bottom of it all.
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