Change of Base Formula Calculator
Use our change of base calculator to find a logarithm with any base. This change of base log calculator shows the change of base formula and helps you find logarithm using change of base formula in a few seconds.
What is the Change of Base Formula?
The change of base formula lets you compute logarithms with any base using a calculator that only supports common logs (base 10) or natural logs (base e).
If you want to change base of log in calculator form, you rewrite logₐ(x) as a ratio of logs with a different base (usually log base 10 or ln base e).
This change of base log calculator helps you find the logarithm using the change of base formula for any argument and any original base.
Change of Base Formula
To find a logarithm using change of base formula, divide the log of the argument by the log of the original base (using any valid new base).
Common choices: b = 10 (log) or b = e (ln).
This is the standard way to find the logarithm using the change of base formula calculator method.
A log change of base calculator works the same with ln.
How to Use the Change of Base Calculator
- 1
Enter the argument x (the number you want the log of).
- 2
Enter the original base a.
- 3
Choose a new base b (or just use base 10 or ln).
- 4
The calculator computes log_a(x) = log_b(x) ÷ log_b(a).
Frequently Asked Questions
log_a(x) = log_b(x) ÷ log_b(a), where b is any valid base.
Use the change of base formula and compute the ratio with log base 10 or natural log (ln).
Yes—this change of base calculator finds log_a(x) using a new base b.
Yes, as long as x > 0 and the base values are > 0 and not equal to 1.
Compute log_b(x) and log_b(a) with the same base b, then divide: log_b(x) ÷ log_b(a).
Most calculators support log base 10 and ln (base e), so b is usually 10 or e.
Because logs are exponents. Rewriting both sides with the same base turns the log into a ratio of exponents, which simplifies to the same value.