Logarithm Calculator
Calculate logarithmic and antilogarithmic values with any base. This calculator can compute logs for base 10 (common logarithm), base e (natural logarithm), and any other positive base.
Calculation Results
Logarithm Result: -
Calculation: -
Common Logarithm Values
| x | log10(x) | x | log10(x) |
|---|---|---|---|
| 1 | 0 | 10 | 1 |
| 2 | 0.3010 | 20 | 1.3010 |
| 3 | 0.4771 | 50 | 1.6990 |
| 4 | 0.6020 | 100 | 2 |
| 5 | 0.6990 | 1000 | 3 |
About the Logarithm Calculator
The logarithm calculator computes both logarithms and antilogarithms with any specified base. Logarithms are the inverse operation of exponentiation and are widely used in mathematics, science, and engineering.
What is a Logarithm?
A logarithm answers the question: "To what power must the base be raised to get this number?" For example:
log10(100) = 2, because 102 = 100
Common Logarithm (Base 10)
The common logarithm uses base 10 and is denoted as log10(x) or simply log(x). It's frequently used in scientific calculations and logarithmic scales like the Richter scale for earthquakes and the decibel scale for sound.
Natural Logarithm (Base e)
The natural logarithm uses the mathematical constant e (≈2.71828) as its base and is denoted as ln(x). It appears naturally in many areas of mathematics, particularly in calculus and complex analysis.
Binary Logarithm (Base 2)
The binary logarithm uses base 2 and is denoted as log2(x). It's important in computer science and information theory, where data is often represented in binary form.
Antilogarithm
An antilogarithm is the inverse operation of a logarithm. It raises the base to the power of the given number. For example:
antilog10(2) = 102 = 100
Logarithmic Identities
Logarithms follow several important mathematical identities:
- logb(xy) = logb(x) + logb(y)
- logb(x/y) = logb(x) - logb(y)
- logb(xy) = y·logb(x)
- logb(b) = 1
- logb(1) = 0