Log Calculator : Logarithm

What is Log ?

Log is short for logarithm, a mathematical function that calculates the power to which a given number (called the base) must be raised to produce a given value. The logarithm of a number "x" to base "b" is written as log_b(x), and represents the exponent to which "b" must be raised to equal "x".

Logarithms are commonly used in mathematics, science, engineering, and finance, among other fields. They are used to simplify calculations, to solve exponential equations, and to perform data compression and analysis. Logarithms are also used in various applications such as audio compression, logarithmic scales, and as a measure of information entropy. Logarithms have inverse functions, called exponentials, and the relationship between logarithms and exponentials can be expressed as log_b(x) = y if and only if b^y = x.

Log Basic formula and Rules

Logarithm (log) formula: logb(x) = y => b^y = x

Rules:

1. logb(b^x) = x, where b > 0 and b ≠ 1
2. logb(1) = 0, where b > 0 and b ≠ 1
3. logb(x/y) = logb(x) - logb(y), where b > 0 and b ≠ 1
4. logb(xy) = logb(x) + logb(y), where b > 0 and b ≠ 1
5. logb(x^y) = y * logb(x), where b > 0 and b ≠ 1
6. logb(a^b) = b * logb(a), where b > 0 and b ≠ 1