Change of Base Calculator
Rewrite any logarithm in the base your calculator supports.
Enter your values
ⓘ Live results
Results
- 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)
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.
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.
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.