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# Log Calculator

To find the logarithm, input the value & base of log, and click the calculate button using log calculator

Table of Contents:

## Log Calculator

Log (Logarithm) calculator is used to calculate logarithm log_{b}x where "b" is the base and "x" is a number. The logarithm of a number x for base b is the elevated exponent b to yield x.

## What is a logarithm?

A logarithm is a mathematical operation that determines the power to which a number, called the base, must be raised to produce a given number. It essentially reverses the process of exponentiation.

More formally, if b^{y} = x, then the logarithm base b of x is y. This relationship is represented as:**log _{b} (x) = y**

Where:

- log denotes the logarithm.
- b is the base.
- x is the number you're taking the logarithm of.
- y is the exponent to which
- b must be raised to get x

**Log base 10**

**Log base 10**

Log10 calculator is a log equation solver used to calculate a log base 10 of the x number, generally lg(x) or log10(x). Log10 calculator is also known as decadic logarithm or common logarithm.

The typical logarithm of x is the power to be increased to be 10 for a value of x. Such as common logarithm of 10 is 1 and for 100 it is 2.

**Log _{10}(x)**

In which 10 is raised to such a number to get the desired value of x

__Log Base 2__

__Log Base 2__

This log equation calculator is used to measure the log base 2 of a number x which is usually written as lb(x) or log_{2}(x).

**Log _{2}(x)**

To get the value of x

Another term binary logarithm is also used for log base 2 calculator. To obtain the value x, the binary logarithm of x is the force to which the number 2 must be lifted.

For example logarithm of 1 will be 0, the binary logarithm of 8 is 3 and the binary logarithm of 4 is 2. It is often used in the philosophy of computer science and knowledge.

## How to calculate a log?

*Example 1:*

*Example 1:*

What is log_{5 }(3125) =?

The question is how many 5 there will need to be multiplied by each other to get 3125.

__Solution:__

5x5x5x5x5=3125

Hence we came to when five 5s are multiplied by each other we get the value 3125.

Log_{5 }(3125) = 5

__Example 2__

__Example 2__

Log (1000) =?

What will be the power of base 10 so the answer will be 1000?

__Solution:__

Log (1000) = 3

Because 10^{3 }=1000

*Example 3*

*Example 3*

Log_{2} 8 =?

So what will be the power of 2 to get the value of x = 8?

__Solution:__

As 2x2x2 = 8

So

Log_{2} 8 = 3