Logarithm Calculator
Logarithm calculator
Compute logarithm of a value with selectable base.
InputsForm2 fieldsLive
Result
3
Using log_b(x) = ln(x) / ln(b).
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Formula
log_b(x) = ln(x) / ln(b) Symbol legend
| Symbol | Meaning | Unit | Copy |
|---|---|---|---|
\log_b(x) | Logarithm of x with base b | number | |
x | Logarithm argument (must be > 0) | number | |
b | Logarithm base (must be > 0 and not 1) | number |
- Validate that x is positive and base b is positive and not 1.
- Take natural log of x and natural log of b.
- Divide ln(x) by ln(b) to get log base b of x.
Example
Worked example: log_10(1000)
- 1 x = 1000, b = 10
- 2 ln(1000) / ln(10) = 3
- 3 log_10(1000) = 3
The logarithm value is 3.
How
- Enter the value x.
- Enter the base b.
- Read the logarithm result and copy it if needed.
Avoid
- Using x <= 0, where logarithm is undefined in real numbers.
- Using base 1, which cannot define a logarithm.
- Confusing log base 10 with natural log base e.
FAQ
Can the base be less than 1?
Yes, as long as it is positive and not equal to 1.
What is the inverse of logarithm?
Exponentiation is the inverse operation of logarithm.
Can I use decimal values for x and base?
Yes. Any positive decimal values are supported with domain checks.
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