Logarithm Calculator
Calculate log base 10, natural log (ln), or any custom base logarithm. Includes the relationship to exponents and antilog values.
How to Use
Select the log type using the tabs. Enter a positive number to calculate its logarithm. For a custom base log, also specify the base.
The Extended Calculator adds a log curve chart, characteristic/mantissa breakdown, and a log rules reference table. The Professional Calculator includes cross-base comparison, logarithmic equation solver, and printable log tables.
Logarithm Formulas
Definition: log_b(x) = y means bʸ = x
Change of base: log_b(x) = ln(x) / ln(b) = log(x) / log(b)
Product rule: log(a × b) = log(a) + log(b)
Quotient rule: log(a / b) = log(a) − log(b)
Power rule: log(xⁿ) = n × log(x)
Worked Example
log₁₀(1000): 10³ = 1000 → 3
ln(e²): e^2 ≈ 7.389 → ln(7.389) = 2
log₂(32): 2⁵ = 32 → 5
Change of base — log₃(81): ln(81)/ln(3) = 4
| Base | Name | log_b(100) |
|---|---|---|
| 2 | Binary | 6.64385619 |
| e | Natural (e) | 4.60517019 |
| 10 | Common (10) | 2 |
| 3 | Base 3 | 4.19180655 |
| 16 | Hex (16) | 1.66096405 |