Log Calculator
Adjust the inputs below. Results update as you type.
How it works
log_b(x) is the exponent to which b must be raised to produce x. log₁₀(1000) = 3 because 10³ = 1000. Natural log uses base e ≈ 2.71828. Change of base: log_b(x) = ln(x)/ln(b). Logarithms convert multiplication to addition, powering to multiplication—core to signal processing, information theory, and compound growth analysis. The decibel scale and Richter scale are logarithmic.
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
A logarithm answers 'what exponent gives this number?': log_b(x) = y means bʸ = x. Common bases are 10 (log) and e (natural log, ln).
Worked example
log₁₀(1000) = 3 because 10³ = 1000. And ln(e²) = 2.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
What is a logarithm?+
The inverse of exponentiation. It tells you the power a base must be raised to in order to produce a given number.
What is the difference between log and ln?+
log usually means base 10; ln is the natural log, base e (≈2.718), which appears throughout growth, decay, and calculus.
How do I change the base?+
Use log_b(x) = ln(x) ÷ ln(b), which converts any base into natural or common logs.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.