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Logarithm

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).

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Logarithm -

Tag(s) : Mathematics

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# Logarithm

## Logarithm Calculator

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).

### What is the natural logarithm?

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.

### What is the decimal logarithm?

The decimal logarithm noted $$\log_{10}$$ 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. $$\log2(x) = \frac {\ln(x)} {\ln(2)}$$