Logarithm Calculator
Calculate logarithms with any base, natural logs, and common logs. Fast, accurate, and easy to use.
Result:
log₁₀(100) = 2
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Formula: logb(x) = y ⇔ by = x
Understanding Logarithms
What is a Logarithm?
A logarithm is the inverse operation to exponentiation. It answers the question: "To what exponent must we raise a base number to obtain another number?"
For example: log₂(8) = 3 because 2³ = 8
Common Logarithms
The common logarithm has a base of 10 (log₁₀). It's frequently used in scientific calculations, pH calculations, and the Richter scale.
Example: log₁₀(1000) = 3
Natural Logarithms
The natural logarithm has a base of e (≈2.71828) and is written as ln(x). It appears in many areas of mathematics, especially calculus and complex analysis.
Example: ln(e³) = 3