📐 Logarithm Calculator
Calculate logarithms with any base
How Logarithm Calculation Works
Formula
log_b(x) = ln(x) / ln(b)
- 1Enter the number (x) you want to find the logarithm of.
- 2Select the base (b): common choices are 10, e (natural), or 2.
- 3The calculator uses the change of base formula: log_b(x) = ln(x) / ln(b).
- 4It computes ln(x) and ln(b) separately, then divides.
- 5Results for log₁₀, ln, and log₂ are also shown for reference.
About Logarithm Calculator
Calculate logarithms with any base. Supports log base 10, natural log (ln), log base 2, and custom bases. Uses the change of base formula with step-by-step explanation.
Frequently Asked Questions
What is a logarithm?
A logarithm answers the question: 'To what power must the base be raised to produce this number?' For example, log₁₀(1000) = 3 because 10³ = 1000.
What is the natural logarithm?
The natural logarithm (ln) uses Euler's number e ≈ 2.71828 as its base. It is widely used in science, engineering, and mathematics because of its unique mathematical properties.
Why can't I take the log of a negative number?
In real number mathematics, logarithms are only defined for positive numbers. The log of zero is negative infinity, and the log of a negative number requires complex numbers.