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How It Works
A logarithm answers the question "to what power must the base be raised to produce x?" The equation y = log₂(x) means b^y = x. This calculator solves for any of the three variables: y (the log), x (the antilog), or the base b.
Example Problem
Find log₁₀(1000):
- We need the power of 10 that gives 1000.
- 10³ = 1000, so log₁₀(1000) = 3.
Frequently Asked Questions
What is the difference between log and ln?
"log" usually means base-10 logarithm (common log), while "ln" means natural log with base e ≈ 2.71828. In some contexts, "log" refers to the natural log. This calculator lets you choose any base.
How to convert between log bases?
Use the change-of-base formula: log₂(x) = ln(x) / ln(b). For example, log₂(8) = ln(8) / ln(2) = 2.079 / 0.693 = 3.
Why can't the base of a logarithm be 1?
Because 1 raised to any power is always 1, the equation 1^y = x has no solution unless x is also 1, and then every y works. A base of 1 makes the logarithm undefined.
Related Calculators
- Natural Log Calculator — solve ln(x) and e^y equations.
- Quadratic Equation Calculator — find roots of second-degree equations.
- Interpolation Calculator — estimate values between data points.
- Statistics Calculator — compute means and standard deviations often used with log-transformed data.
- Z Score Calculator — standardize values, commonly applied after log transformations.