# Logarithm Calculator

## Simple online log calculator - Find log base 2, log base 10, log base 'n', ln (log base e) and log square.

HomeMath

Logarithm

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 LOG10 (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 loga x = y or ay =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 log10(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.

log2 8 = 3
log5 5 = 1
log10 100 = 2
lne e = 1
log7 49 = 2
lne e2 = 2

## Properties of Logorithm

• Product rule

Multiplication of two logarithmic values is equal to the addition of their individual logorithm.
Logb(mn) = logbm + logbn

• Division rule

Division of two logarithmic values is equal to the subtarction of their individual lograthmic. Logb(m/n) = logbm - logbn

• Exponential rule

Logarithm of x with rational exponent is equal to the exponent times its logorithm. Logbx n = nlogbx

• Change of base rule

Change of base rule is the steps to transform the given logorithmic expression with different valid base in quotient form. logbx = logcb / logcx

## 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 log2x.

• Example log2 100

We know that log2100 = log2102
Using product rule log xa = alogx.
So log2102 = 2log210.
2log210 = 2(log 10)2. Since log 10 = 1 which is equal to 2.
So log2 100 is 2.

## Reference Table for Common log and natural log

Notes:

1. E is Eulers number or Eulers constant also known as Base E is 2.718281
2. LN (X) = LOG OF A NUMBER 'X' to BASE E
3. LOG (X) = LOG OF A NUMBER 'X" TO BASE 10
4. LOG2 X = LOG OF A NUMBER 'X" to BASE 2
5. 2 LOG X = LOG OF A NUMBER X TO THE POWER 2 to A BASE 10
6. 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