Logarithm Change of Base Calculator
Compute log base b of x using the change-of-base formula.
Enter your values
Enter the value x you are working with.
Enter the 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_b(x)
- 2.861353
- ln(x)
- 4.60517
- ln(b)
- 1.609438
Quick answer
log_b(x) = ln(x)/ln(b), letting you compute a logarithm in any base using natural or common logs.
log_b(x) = ln(x)/ln(b)
At a glance
| What it does | Compute log base b of x using the change-of-base formula. |
|---|---|
| Category | Math |
| Inputs needed | Value x, Base b |
| Main output | log_b(x) |
| Formula | log_b(x) = ln(x)/ln(b) |
| Cost | Free — no sign-up, no download |
How to use the Logarithm Change of Base Calculator
- 1Enter the value x whose logarithm you want.
- 2Enter the base b you want the logarithm expressed in.
- 3The change-of-base formula divides ln(x) by ln(b) to get log_b(x).
Inputs explained
- Value x
- Enter the value x you are working with.
- Base b
- Enter the base b you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Value x100
- Base b5
Results
- log_b(x)2.861353
- ln(x)4.60517
- ln(b)1.609438
Frequently asked questions
Why can't the base be 1?
log base 1 is undefined since 1 raised to any power is always 1.
Does this work for base 2?
Yes — any positive base other than 1 works, including base 2 for binary logarithms.
What do I need to enter into the Logarithm Change of Base Calculator?
Just 2 values: value x, 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 Change of Base Calculator work out the answer?
log_b(x) = ln(x)/ln(b), letting you compute a logarithm in any base using natural or common logs. 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 Change of Base 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.