Logarithm Calculator
log base 10, natural log and any custom base at once.
Enter your values
ⓘ Live results
Results
- log base 5
- 4.29203
- log₁₀ (common log)
- 3
- ln (natural log)
- 6.907755
- log₂ (binary log)
- 9.965784
- Exponent form
- 5^4.292 = 1000
- Antilog check (10^log₁₀x)
- 1000
Quick answer
log_b(x) answers the question 'b to what power gives x?' — so log₁₀(1000) = 3 because 10³ = 1000.
log_b(x) = ln(x) ÷ ln(b)
How to use the Logarithm Calculator
- 1Enter the number you want the logarithm of — it must be positive.
- 2Enter any custom base you need.
- 3Compare all four bases at once, or copy the exponent form for your working.
Worked example
Using the values the calculator loads with:
Inputs
- Value x1000
- Custom base b5
Results
- log base 54.29203
- log₁₀ (common log)3
- ln (natural log)6.907755
- log₂ (binary log)9.965784
- Exponent form5^4.292 = 1000
- Antilog check (10^log₁₀x)1000
Frequently asked questions
Why can't I take the log of a negative number?
No real power of a positive base gives a negative result, so real logs are defined only for positive inputs.
What is log(1)?
Zero in every base, because any base raised to the power 0 equals 1.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.