Logarithm Calculator Guide: Formula & Worked Example
Short answer
Log of a number to any base, plus ln and log₁₀. In the fixed example below, log_b(x) is 2. Your answer depends on the inputs and assumptions you choose.
Formula
Result = Logarithm Calculator calculation using number, base
The inputs are number, base. Use the input scale shown beside each field and keep time periods and units consistent. Only round the final result for display.
Worked example
- Number
- 100
- Base
- 10
- log_b(x): 2
- ln(x): 4.60517019
- log₁₀(x): 2
- log₂(x): 6.64385619
Understanding the result
Log of a number to any base, plus ln and log₁₀. Start with the base example, then replace each value with the figure that matches your situation.
Number
The example uses 100 for number. This is an illustration, not a recommended value. Keep the unit and time period shown by the field.
Base
The example uses 10 for base. This is an illustration, not a recommended value. Keep the unit and time period shown by the field.
What the comparison means
The comparison changes only number, keeping every other example input fixed. This isolates that input's effect on the primary result. It does not predict future outcomes.
Check units, date boundaries and rounding before using the answer in a report or a practical measurement.
Comparison
| Scenario | Input | Result |
|---|---|---|
| Lower input | Number: 80 | log_b(x): 1.90308999 |
| Base example | Number: 100 | log_b(x): 2 |
| Higher input | Number: 120 | log_b(x): 2.07918125 |
Common mistakes
- Using the wrong units for number.
- Comparing results while changing more than one input at a time.
- Check units, date boundaries and rounding before using the answer in a report or a practical measurement.
Checklist
- Confirm number.
- Confirm base.
- Check the result against your source or provider.
Calculators Percentage Editorial Team
Calculator guides from the Calculators Percentage team. These introductory examples are educational, not professional advice.
Last reviewed:
Check units, date boundaries and rounding before using the answer in a report or a practical measurement.