Logarithm Calculator
log base 10, natural log and any custom base at once.
Enter your values
Enter the value x you are working with.
Enter the custom base b you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)
At a glance
| What it does | log base 10, natural log and any custom base at once. |
|---|---|
| Category | Math |
| Inputs needed | Value x, Custom base b |
| Main output | log base 5 |
| Formula | log_b(x) = ln(x) ÷ ln(b) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Value x
- Enter the value x you are working with.
- Custom base b
- Enter the custom base b you are working with.
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.
What do I need to enter into the Logarithm Calculator?
Just 2 values: value x, custom base b. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Logarithm Calculator work out the answer?
log_b(x) answers the question 'b to what power gives x?' — so log₁₀(1000) = 3 because 10³ = 1000. It applies the formula log_b(x) = ln(x) ÷ ln(b) and shows the working so you can check each step by hand.
Is the Logarithm Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.