**Log calculator** finds the logarithm function result (can be called exponent) from the given base number and a real number.

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**b: ** log base number, b>0 and b≠1 / **x: ** is real number, x>0

**logb(x) = y**, and **x = logb(bx)****logb(x) = y** and **x = by**

## Logarithm

**Logarithm** is considered to be one of the basic concepts in mathematics.There are plenty of definitions, starting from really complicated and ending up with rather simple ones.In order to answer a question, what a logarithm is, let"s take a look at the table below:

21 | 22 | 23 | 24 | 25 | 26 |

2 | 4 | 8 | 16 | 32 | 64 |

This is the table in which we can see the values of two squared, two cubed, and so on.This is an operation in mathematics, known as **exponentiation**.If we look at the numbers at the bottom line, we can try to find the power value to which 2 must be raised to get this number.For example, to get 16, it is necessary to raise two to the fourth power.And to get a 64, you need to raise two to the sixth power.

Therefore, **logarithm is the exponent to which it is necessary to raise a fixed number** (which is called the base), to get the number y.In other words, a logarithm can be represented as the following:

logb x = y

with b being the base, x being a real number, and y being an exponent.

For example, 23 = 8 ⇒ log2 8 = 3 (the logarithm of 8 to base 2 is equal to 3, because 23 = 8).Similarly, log2 64 = 6, because 26 = 64.

Therefore, it is obvious that **logarithm operation is an inverse one to exponentiation**.

21 | 22 | 23 | 24 | 25 | 26 |

2 | 4 | 8 | 16 | 32 | 64 |

log22 = 1 | log24 = 2 | log28 = 3 | log216 = 4 | log232 = 5 | log264 = 6 |

Unfortunately, not all logarithms can be calculated that easily.For example, finding log2 5 is hardly possible by just using our simple calculation abilities.After using logarithm calculator, we can find out that

log2 5 = 2,32192809

There are a few specific types of logarithms.For example, the logarithm to base 2 is known as the binary logarithm,and it is widely used in computer science and programming languages.The logarithm to base 10 is usually referred to as the common logarithm,and it has a huge number of applications in engineering, scientific research, technology, etc.Finally, so called natural logarithm uses the number e (which is approximately equal to 2.71828) as its base,and this kind of logarithm has a great importance in mathematics, physics,and other precise sciences.

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The **logarithm** logb(x) = y is read as log base b of x is equals to y.Please note that the **base of log** number b must be greater than 0 and must not be equal to 1.And the number (x) which we are calculating **log** base of (b) must be a positive real number.