Logarithm Calculator
log_b(x) = ln(x)/ln(b). Click any i for detail.
Log
x
i
Argument
Must be positive. |
|
|---|---|
Base b
i
Base
Positive and not 1. 10 is common log; e ≈ 2.718 is natural log. |
How to use this calculator
- Enter x > 0 and base b > 0, b ≠ 1.
- Read log base b of x.
- Check ln(x) and log₁₀(x) in the breakdown.
- Use change-of-base when your calculator only has ln.
Results explained
Logarithms answer “to what power must b be raised to get x?” Change-of-base uses natural logs: log_b(x) = ln(x)/ln(b).
Quick reference: logs
log₁₀(1000) = 3 because 10³ = 1000.
| Item | Detail |
|---|---|
| Common log | base 10 |
| Natural log | base e ≈ 2.718 |
| Change of base | ln x / ln b |
| Domain | x must be positive |
log of zero or negatives is undefined on the reals.
How the estimate is built
log_b(x) = ln(x) / ln(b).
Example scenario
log₁₀(1000) → 3.
FAQ
How do I get ln without typing e?
Read the ln line in the breakdown, or set base to 2.718281828.
Why can't b be 1?
1 raised to any power is still 1; log base 1 is not defined.
Are log and exp inverses?
Yes. log_b(b^x) = x and b^(log_b x) = x for valid x.