Logarithm Calculator
Simple online log calculator - Find log base 2, log base 10, log base 'n', ln (log base e) and log square.
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 + logbnDivision 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:
- 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.
