Numbers
Calculateur de logarithmes
Used by developers, writers, and creators worldwide.
A logarithm calculator finds the logarithm of a number in any base, along with the natural and common logarithms for reference. Enter a positive value and a base of two or more and it returns the logarithm in your chosen base using the change-of-base formula, the natural log to base e, and the base-ten common log, each to six decimals, plus a check that raising the base to the result recovers your value. Logarithms answer the question of what exponent a base must be raised to in order to reach a number, and they appear in compound growth, sound intensity in decibels, the pH scale, the Richter scale, and algorithm analysis. Students use the tool to check homework and learn the change-of-base trick, while scientists use it for quick values. The reverse-check line makes the logarithm concrete. Use it to evaluate a log in any base.
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How to use
- Choose your options above
- Click Generate
- Copy your result
Detailed instructions
- Enter the positive value to take the log of.
- Enter the base you want to use.
- Click Generate to compute the logarithm.
- Read the natural and common logs alongside it.
Use Cases
- •Evaluating a logarithm in a custom base
- •Checking natural and common log homework
- •Applying the change-of-base formula
- •Working with decibel, pH, or Richter scales
- •Analysing growth and algorithm complexity
Tips
- →Logarithms are only defined for positive values.
- →Use change of base to get any base from ln.
- →Natural log uses base e; common log uses base ten.
- →The reverse-power check confirms the result.
FAQ
what is the change-of-base formula
To find a log in base b, divide the natural log of the value by the natural log of the base: log_b(x) equals ln(x) over ln(b). This lets a calculator that only knows natural and common logs compute any base.
why must the value be positive
Logarithms are only defined for positive numbers, because no real exponent can raise a positive base to zero or a negative result. The tool keeps the value positive so the output stays real and meaningful.
what is the difference between ln and log
Natural log, written ln, uses the base e, about 2.718, and arises in continuous growth. Common log, written log or log10, uses base ten and suits scales built on powers of ten such as decibels and pH.
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