Math

Logarithm Calculator

Calculate logarithms in any base.

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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

log_b(x) = ln(x) / ln(b)

Usage examples

Review a ready-made scenario, copy it, then tweak inputs to match your case.

Example

2 inputs3 outputs

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

5 of 5 rows
ValueLog resultLog₁₀
1011
501.71.7
10022
2002.32.3
1,00033

Logarithms grow very slowly compared to the input values.

Logarithmic curve

Highest: 1,000 (3)Lowest: 10 (1)
ValueLog result

Focus point

10

1

Position

#1 of 5

Original order

Share of total

10%

Total: 10

PositiveNegative

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.