Logarithm Calculator
log base 10, natural log and any custom base.
Enter your values
Enter the number you are working with.
Enter the base 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 10
- 3
- Natural log (ln)
- 6.90775528
- log base 10
- 3
- log base 2
- 9.96578428
Working
- 1log_10(1000) = ln 1000 ÷ ln 10 = 3
Quick answer
A logarithm answers 'what power of the base gives this number?' — log_b(x) = ln(x) ÷ ln(b).
log_b(x) = ln x ÷ ln b
At a glance
| What it does | log base 10, natural log and any custom base. |
|---|---|
| Category | Math |
| Inputs needed | Number, Base |
| Main output | log base 10 |
| Formula | log_b(x) = ln x ÷ ln b |
| Cost | Free — no sign-up, no download |
How to use the Logarithm Calculator
- 1Enter the number.
- 2Enter the base you want.
- 3Read the log in your base and the common alternatives.
Inputs explained
- Number
- Enter the number you are working with.
- Base
- Enter the base you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Number1000
- Base10
Results
- log base 103
- Natural log (ln)6.90775528
- log base 103
- log base 29.96578428
- log_10(1000) = ln 1000 ÷ ln 10 = 3
Frequently asked questions
What is the natural log?
The logarithm to base e (2.71828…), which appears wherever continuous growth or decay is modelled.
Why can't you log a negative number?
No real power of a positive base produces a negative result, so real logs are only defined for positive inputs.
What do I need to enter into the Logarithm Calculator?
Just 2 values: number, base. 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?
A logarithm answers 'what power of the base gives this number?' — log_b(x) = ln(x) ÷ ln(b). 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.