Log Calculator (Logarithm)
Calculate logarithms, anti-logarithms, and visualize logarithmic functions
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Logarithm
Anti-Logarithm
Natural Log
Logarithm Calculator
Enter values and click Calculate
Anti-Logarithm Calculator
Enter values and click Calculate
Natural Logarithm Calculator
Enter values and click Calculate
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Logarithmic Function Visualization
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About Logarithms
What is a Logarithm?
A logarithm is the inverse operation to exponentiation. The logarithm of a number x to the base b is the exponent to which b must be raised to produce x.
logb(x) = y ⟺ by = x
For example, log10(1000) = 3 because 103 = 1000.
Common Logarithm Bases
- Common Logarithm (Base 10): log10(x) - Often used in engineering and for pH calculations
- Natural Logarithm (Base e): ln(x) or loge(x) - Used in mathematics and physics
- Binary Logarithm (Base 2): log2(x) - Used in computer science and information theory
Logarithm Properties
logb(x ⋅ y) = logb(x) + logb(y)
logb(x / y) = logb(x) - logb(y)
logb(xy) = y ⋅ logb(x)
logb(b) = 1
logb(1) = 0
Real-World Applications
- Earthquake measurement: The Richter scale is logarithmic
- Chemistry: pH values represent hydrogen ion concentration on a logarithmic scale
- Computer science: Algorithm complexity is often expressed using big O notation with logarithms
- Finance: Compound interest calculations use logarithmic functions
- Biology: The Weber-Fechner law describes logarithmic relationships between stimuli and perception