Logarithm Calculator
Calculate logarithms with any base. Supports common log (base 10), natural log (base e), binary log (base 2), and custom bases.
Calculate Logarithm
Select the logarithm type and enter a number
Result
Enter a number to calculate its logarithm
Logarithm Reference
Common Log (log₁₀)
log₁₀(1) = 0
log₁₀(10) = 1
log₁₀(100) = 2
log₁₀(1000) = 3
Natural Log (ln)
ln(1) = 0
ln(e) ≈ 1
ln(10) ≈ 2.303
e ≈ 2.71828
Binary Log (log₂)
log₂(1) = 0
log₂(2) = 1
log₂(8) = 3
log₂(1024) = 10
Frequently Asked Questions
What is a logarithm?
A logarithm answers: what power must we raise the base to get a number? For example, log₁₀(100) = 2 because 10² = 100.
What is the natural logarithm?
The natural logarithm (ln) uses Eulers number e (≈ 2.71828) as its base. It appears frequently in calculus and physics.
How do I convert between logarithm bases?
Use the change of base formula: logₐ(x) = ln(x) / ln(a) = log₁₀(x) / log₁₀(a).
Related Calculators
Math
Fraction Calculator
Add, subtract, multiply, and divide fractions
Math
Scientific Calculator
Advanced calculator with scientific functions
Math
Statistics Calculator
Calculate mean, median, mode, standard deviation, and more
Math
Probability Calculator
Calculate probabilities, combinations, and permutations
Math
Pythagorean Theorem Calculator
Calculate right triangle sides using a² + b² = c²
Math
Long Division Calculator
Calculate division with step-by-step work shown