How to Calculate Logarithm Calculator
What is Logarithm Calculator?
A logarithm calculator computes log base 10, natural log (ln), log base 2, and any other base. Logarithms are the inverse of exponentiation.
Formula
log_b(x) = y means b^y = x; Change of base: log_b(x) = log_10(x) / log_10(b)
- x
- Number
- b
- Base — Usually 10, e, or 2
- y
- Logarithm result
Step-by-Step Guide
- 1logₐ(x) = y means aʸ = x
- 2log₁₀(x): common logarithm
- 3ln(x): natural log, base e ≈ 2.71828
- 4Change of base: logₐ(x) = ln(x)/ln(a)
Worked Examples
Input
log₁₀(1000)
Result
3 (because 10³ = 1000)
Input
ln(e²)
Result
2
Frequently Asked Questions
What's the difference between log, ln, and log₁₀?
log (no base) = log₁₀. ln = natural log (base e ≈ 2.718). log₂ = binary logarithm.
When do I use logarithms?
Solving exponential equations, measuring scales (pH, Richter, decibels), growth/decay rates.
Why is log₁₀ of 1000 equal to 3?
10³ = 1000, so log₁₀(1000) = 3. Logarithm is the inverse of exponentiation.