What Is a Logarithm?

In mathematics, logarithm is the inverse of exponentiation, just as division is the inverse of multiplication, and vice versa. This means that the logarithm of a number is an exponent that must produce another fixed number (base). In simple cases, the log count factor in a multiplier. More generally, powers allow any positive real number to be raised to any real power, always yielding a positive result, so the logarithm can be calculated for any two positive real numbers b and x where b is not equal to 1.

The logarithm of N to a

. The logarithmic symbol log is from the Latin logarithm, first used by Italian mathematicians

in case

, That is, the x- th power of a is equal to N ( a > 0, and a 1), then the number x is called the logarithm of N with a as the base, and is recorded as

. Where a is called logarithmic

definition

function

Called

Logarithm has many applications both inside and outside of mathematics. Some of these events are related to the concept of scale invariance. For example, each chamber of a nautilus shell is a rough copy of the next, scaled by a constant factor. This gives rise to a logarithmic spiral. Benford's law on leading number allocation can also be explained by scale invariance. Logarithms are also related to self-similarity. For example, the logarithmic algorithm appears in algorithm analysis, which solves the problem by breaking the algorithm into two similar smaller problems and patching its solution. The dimensions of self-similar geometries, that is, parts that resemble the overall image are also based on logarithms. A logarithmic scale is useful for quantifying the relative change in a value that is the opposite of its absolute difference. In addition, since the logarithmic function log (x) grows very slowly for large x, a logarithmic scale is used to compress large-scale scientific data. Logarithms also appear in many scientific formulas, such as the Tsiolkovsky rocket equation, the Fenske equation, or the Nernst equation. ^[5]