Change of Base Calculator
Rewrite any logarithm in the base your calculator supports.
Enter your values
Enter the argument x you are working with.
Enter the original base b you are working with.
Enter the new base c 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_7(50)
- 2.010382
- Rewritten form
- log_10(50) ÷ log_10(7)
- Numerator
- 1.69897
- Denominator
- 0.845098
- Check with natural logs
- 2.010382
Working
- 11.69897 ÷ 0.8451 = 2.01038
Quick answer
The change of base rule says log_b(x) = log_c(x) ÷ log_c(b), so any logarithm can be evaluated with ln or log₁₀.
log_b(x) = log_c(x) ÷ log_c(b)
At a glance
| What it does | Rewrite any logarithm in the base your calculator supports. |
|---|---|
| Category | Math |
| Inputs needed | Argument x, Original base b, New base c |
| Main output | log_7(50) |
| Formula | log_b(x) = log_c(x) ÷ log_c(b) |
| Cost | Free — no sign-up, no download |
How to use the Change of Base Calculator
- 1Enter the argument and its original base.
- 2Choose the base your calculator can handle — 10 or e.
- 3Copy the rewritten division and evaluate it.
Inputs explained
- Argument x
- Enter the argument x you are working with.
- Original base b
- Enter the original base b you are working with.
- New base c
- Enter the new base c you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Argument x50
- Original base b7
- New base c10
Results
- log_7(50)2.010382
- Rewritten formlog_10(50) ÷ log_10(7)
- Numerator1.69897
- Denominator0.845098
- Check with natural logs2.010382
- 1.69897 ÷ 0.8451 = 2.01038
Frequently asked questions
Does the new base matter?
No — any base gives the same answer, which is why ln and log₁₀ are both fine.
Where does this come up?
Any time you need log base 2 or base 7 on a calculator that only offers log and ln.
What do I need to enter into the Change of Base Calculator?
Just 3 values: argument x, original base b, new base c. 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 Change of Base Calculator work out the answer?
The change of base rule says log_b(x) = log_c(x) ÷ log_c(b), so any logarithm can be evaluated with ln or log₁₀. It applies the formula log_b(x) = log_c(x) ÷ log_c(b) and shows the working so you can check each step by hand.
Is the 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.