- Logarithm
- 3
How it works
A negative logarithm can be valid
log₁₀(0.01) equals −2 because 10⁻² = 0.01. A negative answer does not imply an invalid input: with a base greater than one, positive arguments below one naturally produce negative logarithms.
Choosing the logarithm base
A logarithm asks which exponent gives the entered argument for a chosen base. Changing the base changes the result, even though the argument stays the same. Use the missing-base or missing-argument mode only when those are the unknown quantities in your problem. Check the real logarithm domain before calculating; not every combination of signs and base values is valid.
Logarithm: formula and assumptions
log_b(x) = ln(x) / ln(b).
The argument and base must be positive, and the base cannot equal one.
Solve base or argument: formula and assumptions
If log_b(x)=y, then x=b^y and b=x^(1/y).
A valid base is positive and different from one. Some zero or unit inputs do not give a unique inverse.
Worked example
Using the Logarithm example:
- Number
- 1000
- Base
- 10
log_b(x) = ln(x) / ln(b).
Example result
Logarithm: 3
These are illustrative inputs. Change the values to explore a different scenario.
Formula references
References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.
Common questions
Why can the logarithm base not equal one?
Every power of one is one, so base one cannot provide the one-to-one relationship required for a logarithm.
How do I solve for the argument from a logarithm?
If log base b of x equals y, then x = b^y. The base must be positive and different from one.
Prepared by Finflo. See our methodology and editorial policy.