### Log Base 2 Calculator

The online Log Base 2 Calculator is used to calculate the log base 2 of a number x, which is generally written as lb(x) or log2(x). Log base 2, also known as the binary logarithm, is the logarithm to the base 2. The binary logarithm of x is the power to which the number 2 must be raised to obtain the value x. For example, the binary logarithm of 1 is 0, the binary logarithm of 2 is 1 and the binary logarithm of 4 is 2. It is often used in computer science and information theory.

### The Humble Logarithm

Every semester I teach calculus I ask my students if they know why we care about logarithms. And every semester I am met with a sea of blank faces and shoulder shrugs. "What is the most important property logs have?" "What is the logarithm of a product?" Logarithms turn products into sums.

### The 17 equations that changed the course of history

Mathematics is all around us, and it has shaped our understanding of the world in countless ways. In 2013, mathematician and science author Ian Stewart published a book on 17 Equations That Changed The World. We recently came across this convenient table on Dr. Paul Coxon's twitter account by mathematics tutor and blogger Larry Phillips that summarizes the equations. For example, a right triangle drawn on the surface of a sphere need not follow the Pythagorean theorem. A logarithm for a particular base tells you what power you need to raise that base to to get a number.

### The Naive Bayes Classifier explained

With the Naive Bayes model, we do not take only a small set of positive and negative words into account, but all words the NB Classifier was trained with, i.e. all words presents in the training set. If a word has not appeared in the training set, we have no data available and apply Laplacian smoothing (use 1 instead of the conditional probability of the word). The probability a document belongs to a class C is given by the class probability P(C) multiplied by the products of the conditional probabilities of each word for that class. In theory we want a training set as large as possible, since that will increase the accuracy. Taking the n-th power of such a large number, will definitely result in computational problems, so we should normalize it.

### PAC-Bayes Iterated Logarithm Bounds for Martingale Mixtures

We give tight concentration bounds for mixtures of martingales that are simultaneously uniform over (a) mixture distributions, in a PAC-Bayes sense; and (b) all finite times. These bounds are proved in terms of the martingale variance, extending classical Bernstein inequalities, and sharpening and simplifying prior work.