You can input a number and find the log of the number for any base or Ln of the number. You can also enter the log value and find the reverse log for a given base

This is equivalent to writing 10 ^{ 2 } = 100

OR LOG_{10 } (100) = 2

## How to use the logarithmic calculator tool?

The default configuration is log base 10 calculator or log10 calculator (or the common log)

Enter the input value in the input field

The log square and the log value for base 10 is automatically shown in the output fields

Log base 2 calculator or simply log2 calculator

Change the base value to 2 and you can see the output reflecting the base 2 value.

Ln Calculator or Log Base E Calculator or the Natural Log Calculator

To use this as ln calculator, select the base E option or enter the base E value of 2.718281 and you can compute the ln values of any input

Log Base Calculator to any base

To use this with any base like Log Base 3, Log Base 4, enter the base value which is desired and it will automatically compute the log of that number

Reverse Log Calculator / Inverse Log Calculator

Set the base value, enter the log value in output field, the reverse / inverse value is automatically shown in input field

## What is Logarithm?

Definition of Logarithm

Logarithm is an inverse (opposite) function of exponent function.Logarithm is the power to which the number must be raised to get some other number.

Notation:

Logarithm is denoted by log_{a}x = y or a^{y}=x,

Which is read as Logarithm of x to the base a is equal to y

where a is the base.What is Natural Logarithm?

The natural log is nothing but the log with base 'e' and is denoted by ln

The term 'e' is called Euler's constant and it has a value of 2.718281

What is Common Logarithm?

The common log is usually log with base '10' and is denoted by log

_{10}(x)We can find the log of a number with any base by computing the log of number and the log of the base to base 10 log (number)/ log (base)

Logarithm of few numbers with different base.

log

_{2}8 = 3

log_{5}5 = 1

log_{10}100 = 2

ln_{e}e = 1

log_{7}49 = 2

ln_{e}e^{2}= 2

## Properties of Logorithm

Product rule

Multiplication of two logarithmic values is equal to the addition of their individual logorithm.

Log_{b}(mn) = log_{b}m + log_{b}nDivision rule

Division of two logarithmic values is equal to the subtarction of their individual lograthmic. Log

_{b}(m/n) = log_{b}m - log_{b}nExponential rule

Logarithm of x with rational exponent is equal to the exponent times its logorithm. Log

_{b}x^{n}= nlog_{b}xChange of base rule

Change of base rule is the steps to transform the given logorithmic expression with different valid base in quotient form. log

_{b}x = log_{c}b / log_{c}x

## What is Log Square?

Log Square

Log square is just the square of the respective log number.It is denoted by (log x)

^{2}or log^{2}x.Example log

^{2}100We know that log

^{2}100 = log^{2}10^{2}

Using product rule log x^{a}= alogx.

So log^{2}10^{2}= 2log^{2}10.

2log^{2}10 = 2(log 10)^{2}. Since log 10 = 1 which is equal to 2.

So log^{2}100 is 2.

## Reference Table for Common log and natural log

Notes:

- E is Eulers number or Eulers constant also known as Base E is 2.718281
- LN (X) = LOG OF A NUMBER 'X' to BASE E
- LOG (X) = LOG OF A NUMBER 'X" TO BASE 10
- LOG2 X = LOG OF A NUMBER 'X" to BASE 2
- 2 LOG X = LOG OF A NUMBER X TO THE POWER 2 to A BASE 10
- 3 LN X = LOG OF A NUMBER TO THE POWER OF 3 to BASE E

Term | Expansion | Base | Input | Log Result Output | Log Square |
---|---|---|---|---|---|

LN(10) | LN 10 Base E | 2.718281 | 10 | 2.303 | 5.304 |

LN(2) | LN 2 Base E | 2.718281 | 2 | 0.693 | 0.480 |

LN(1) | LN 1 Base E | 2.718281 | 1 | 0 | 0 |

LN(E) | LN E Base E | 2.718281 | 2.718281 | 1 | 1 |

LN 0 | LN 0 Base E | 2.718281 | 0 | not defined | not defined |

LOG(E) | Log E Base 10 | 10 | 2.718281 | 0.434 | 0.189 |

LOG10 E | Log E Base 10 | 10 | 2.718281 | 0.434 | 0.189 |

LOG2 E | Log 2 Base 10 | 10 | 2 | 0.301 | 0.091 |

LOG(10) | Log 10 Base 10 | 10 | 10 | 1 | 1 |

LOG(2) | Log 2 Base 10 | 10 | 2 | 0.301 | 0.091 |

log 0.1 | Log 0.1 Base 10 | 10 | 0.1 | -1 | 1 |

LOG 0.5 | Log 0.5 Base 10 | 10 | 0.5 | -0.301 | 0.091 |

LOG 1 | Log 1 Base 10 | 10 | 1 | 0 | 0 |

LOG 2 | Log 2 Base 10 | 10 | 2 | 0.301 | 0.091 |

LOG 3 | Log 3 Base 10 | 10 | 3 | 0.477 | 0.228 |

LOG 4 | Log 4 Base 10 | 10 | 4 | 0.602 | 0.362 |

LOG 5 | Log 5 Base 10 | 10 | 5 | 0.699 | 0.489 |

LOG 6 | Log 6 Base 10 | 10 | 6 | 0.778 | 0.606 |

LOG 7 | Log 7 Base 10 | 10 | 7 | 0.845 | 0.714 |

LOG 8 | Log 8 Base 10 | 10 | 8 | 0.903 | 0.816 |

LOG 9 | Log 9 Base 10 | 10 | 9 | 0.954 | 0.911 |

LOG 10 | Log 10 Base 10 | 10 | 10 | 1 | 1 |

LOG 11 | Log 11 Base 10 | 10 | 11 | 1.041 | 1.084 |

LOG 25 | Log 25 Base 10 | 10 | 25 | 1.398 | 1.954 |

LOG 32 | Log 32 Base 10 | 10 | 32 | 1.505 | 2.265 |

LOG 100 | Log 100 Base 10 | 10 | 100 | 2 | 4 |

LOG 1000 | Log 1000 Base 10 | 10 | 1000 | 3 | 9 |

log 10000 | Log 10000 Base 10 | 10 | 10000 | 4 | 16 |

LOG2(2) | Log 2 Base 2 | 2 | 2 | 1 | 1 |

LOG2(8) | Log 8 Base 2 | 2 | 8 | 3 | 9 |

log2 3 | Log 3 Base 2 | 2 | 3 | 1.585 | 2.512 |

log2 5 | Log 5 Base 2 | 2 | 5 | 2.322 | 5.391 |

2 LN 2 | Log (2 to POWER 2) Base E | 10 | 4 | 1.386 | 1.922 |

3 ln 5 | Log 5 to POWER 3) Base E | 10 | 125 | 4.828 | 23.313 |

## Frequently Asked Questions on Logarithmic Calculator

Only difference is with base value.

Log refered to base 10. Ln refered to base e.

The value of e in log is equal to 2.718281.

Natural logarithm is the logarithm with base 'e'.Common logarithm is logarithm is with base 10.

No, we dont have logarithm for a negative number.

More over log is function is only defined for positive numbers.

Log 0 is with any base is not defined and log function is defined only for values greater than 0.

Log of a given number is calculated by using log table by finding characteristic part and mantissa part.

We need to use the respective log table to get the log value.