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Tool for calculating logarithms. The logarithm function is denoted log or ln and is defined by a base (the base e for the natural logarithm).

Answers to Questions

What is the natural logarithm? (Definition)

The definition of the natural logarithm is the function whose derivative is the inverse function of \( x \mapsto \frac 1 x \) defined for \( x \in \mathbb{R}_+^* \).

The natural logarithm is noted \( \log \) or \( \ln \) and is based on the number \( e \approx 2.71828\ldots \) (see decimals of number e).

Example: \( \Log(e) = \ln(e) = 1 \)

Example: \( \Log(1) = \ln(1) = 0 \)

Some people use \( \log \) for \( \log_{10} \), so make sure to know which notation is used.

What is the neperian logarithm?

The neperian logarithm is the other name of the natural logarithm (with base e).

What is the decimal logarithm?

The decimal logarithm noted \( \log_{10} \) or log10 is the base \( 10 \) logarithm. This is one of the most used logarithms in calculations and logarithmic scales. $$ \log_{10}(x) = \frac { \ln(x)} { \ln(10) } $$

Example: \( \log_{10}(1000) = 3 \)

What is the binary logarithm?

The binary logarithm noted \( \log_{2} \) (or sometimes \( lb \)) is the base \( 2 \) logarithm. This logarithm is used primarily for computer calculations. $$ \log2(x) = \frac {\ln(x)} {\ln(2)} $$

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