Inputs
Adjust the assumptions to match your scenario. Results update instantly.
Results
Primary outputs and comparison insights are built from the current inputs.
Log result
2
Logarithm of value in the specified base.
Log₁₀
2
Common logarithm (base 10).
Natural log (ln)
4.61
Natural logarithm (base e).
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How this calculator works
The Logarithm Calculator computes logarithms in any base, plus common (log₁₀) and natural (ln) logarithms. Enter value and base to estimate log result, log₁₀, and natural log (ln). The calculator updates instantly and adds a comparison table plus chart so you can test the sensitivity of the result before you use it in a decision.
Quick guide
Jump straight to the section you need, then return to the calculator.
Inputs
- The number to find the logarithm of.
- Logarithm base (e.g. 10, 2, or 2.718 for natural).
Outputs
- Logarithm of value in the specified base.
- Common logarithm (base 10).
- Natural logarithm (base e).
Assumptions
- Value must be positive.
- Base must be positive and not equal to 1.
Tips
- log₁₀(1000) = 3 because 10³ = 1000.
- Natural log (ln) uses base e ≈ 2.718.
Formula guide
Use these formulas to audit the output or explain it to someone else.
1 formulas
Usage examples
Review a ready-made scenario, copy it, then tweak inputs to match your case.
Example
Common log check
Inputs
- Example input Value: 1,000
- Example input Base: 10
Outputs
- Example result Log result: 3
- Example result Log₁₀: 3
- Example result Natural log (ln): 6.91
log₁₀(1000) = 3, a quick way to count the number of digits minus one.
Log by value
| Value | Log result | Log₁₀ |
|---|---|---|
| 10 | 1 | 1 |
| 50 | 1.7 | 1.7 |
| 100 | 2 | 2 |
| 200 | 2.3 | 2.3 |
| 1,000 | 3 | 3 |
Logarithms grow very slowly compared to the input values.
Logarithmic curve
Focus point
10
1
Position
#1 of 5
Original order
Share of total
10%
Total: 10
Logarithms grow very slowly compared to the input values.
References
- Logarithm change of base formula
- Properties of logarithms
FAQ
Common questions
What does the Logarithm Calculator do?
The Logarithm Calculator computes logarithms in any base, plus common (log₁₀) and natural (ln) logarithms. Enter value and base to estimate log result, log₁₀, and natural log (ln). The calculator updates instantly and adds a comparison table plus chart so you can test the sensitivity of the result before you use it in a decision. It is part of our math toolkit.
What inputs do I need?
Typical inputs include The number to find the logarithm of., Logarithm base (e.g. 10, 2, or 2.718 for natural)..
How are the results calculated?
We follow the formulas and assumptions outlined in the "How this calculator works" section. You will see outputs like Logarithm of value in the specified base., Common logarithm (base 10)., Natural logarithm (base e)..
Can I share or download the results?
Use the Copy link or Print buttons to share your results. If a table or chart appears, you can download the data as CSV.
Is my data stored?
No. Calculations run in your browser and we do not store your inputs.
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