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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

## Logarithm Expression Simplifier

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? (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 and bad calculators 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 (log10)?

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 (log2)?

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

Use the formula above to calculate a log2 with a calculator with only the log key.

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