 # Find Log of a Number (Logarithm Calculator)

## Simple online log calculator - Use it as log base 2 calculator, log base 10, log base 'n', ln calculator (log base e) and also to find 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

## What is Logarithm? • ### 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

## 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

## How to do 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

## Frequently Asked Questions on Logarithmic Calculator 