Log Calculator
Calculate logarithms with any base. Supports common log (base 10), natural log (base e), and custom base logarithms with instant results.
How to Use This Log Calculator
- Choose the logarithm type: Log₁₀ (common), Ln (natural), or Custom Base.
- If using custom base, enter the base value (must be greater than 1).
- Enter the number you want to find the logarithm of (must be positive).
- Click "Calculate Logarithm" to see the result.
Logarithm Formulas
Common Logarithm Values
| x | log₁₀(x) | ln(x) | log₂(x) |
|---|---|---|---|
| 1 | 0 | 0 | 0 |
| 2 | 0.301 | 0.693 | 1 |
| 10 | 1 | 2.303 | 3.322 |
| 100 | 2 | 4.605 | 6.644 |
| 1000 | 3 | 6.908 | 9.966 |
Examples
log₁₀(1000) = ?
10^3 = 1000, so log₁₀(1000) = 3
ln(e²) = ?
ln(e²) = 2 because e^2 = e²
log₂(32) = ?
2^5 = 32, so log₂(32) = 5
Frequently Asked Questions
What is the difference between log and ln?
log typically refers to log base 10 (common logarithm), while ln refers to log base e (natural logarithm). Common logs are useful for orders of magnitude, while natural logs appear frequently in calculus and growth/decay problems.
Can you take the log of a negative number?
No, the logarithm of a negative number is not a real number. Logarithms are only defined for positive real numbers. In complex mathematics, log of negative numbers involves imaginary numbers, but this calculator works with real numbers only.
What is log of 0?
The logarithm of 0 is undefined (negative infinity). As x approaches 0 from the positive side, log(x) approaches negative infinity. There is no real number y such that b^y = 0 for any base b.