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Log Calculator
Log CalculatorLogarithm
Multi-Base Computational Engine
About the Log Calculator
Calculate logarithms to base 10, base 2, the natural logarithm (base e) or any custom base.
How to use the Log Calculator
- Enter the Input Value (x), which must be positive.
- Choose LOGββ, LN(e), LOGβ or CUSTOM and enter the Base (b) if needed.
- Press Calculate.
Formula and method
log_b(x) = y means bΚΈ = x. Change of base: log_b(x) = ln(x) Γ· ln(b).
Worked example
logββ(1,000) = 3, logβ(8) = 3 and ln(e) = 1.
Common logs. logββ(1,000) = 3, because 10Β³ = 1,000. And ln(e) = 1.
When to use the Log Calculator
- Solving equations where the unknown is an exponent.
- Working with pH, decibels and earthquake magnitudes.
- Converting between logarithm bases.
Common mistakes to avoid
- Trying to take the logarithm of zero or a negative number.
- Mixing up log (base 10) and ln (base e).
Tips
- The logarithm of a non-positive number is not defined for real numbers.
- log(a Γ b) = log a + log b.
Frequently Asked Questions
A logarithm to base e, where e β 2.71828.
log_b(x) = log(x) Γ· log(b), using any base for the two logs on the right.
They turn multiplication into addition and let us handle huge ranges of values on a manageable scale.