Logarithmic paper

Logarithmic paper (also logarithmic paper ) belongs to the class of mathematical papers (also: network paper) and is covered with a coordinate network, so that coordinates can be displayed on it in a simple way.

The logarithmic axis division can be used for either or both axes .

The importance of such special papers is decreasing due to the possibility of generating graphic representations from computer programs .

Logarithmic paper

Single logarithmic paper or semi-logarithmic paper is provided with a special coordinate network that is divided logarithmically either horizontally or vertically . This means that the actual dimension is the logarithm of the number written on it.

Single logarithmic paper, horizontally divided logarithmically

Single logarithmic paper, vertically divided logarithmically

In the case of horizontal single-logarithmic paper, logarithmic functions are represented as straight lines. With perpendicular logarithmic paper, exponential functions are represented as straight lines, because from follows . ${\ displaystyle y = \ log _ {a} x}$ ${\ displaystyle y = a ^ {x}}$ ${\ displaystyle y = a ^ {x}}$ ${\ displaystyle \ log (y) = x \ log (a)}$

The special paper enables such functions to be drawn easily or to check whether the given value pairs match such a function (they must then lie on a straight line).

Examples

In the following, the functions are shown with the equations and on horizontal simple logarithmic paper. ${\ displaystyle y = \ log _ {e} (x) = \ ln (x)}$ ${\ displaystyle y = \ log _ {10} (x) = \ lg (x)}$

In the following the functions are shown with the equations and on straight logarithmic paper. ${\ displaystyle y = 10 ^ {x}}$ ${\ displaystyle y = 2 ^ {x}}$

Double logarithmic paper

Double logarithmic paper is provided with a special coordinate network that is logarithmically divided both horizontally and vertically . This means that the actual dimension is the logarithm of the number written on it.

With logarithmic paper, power functions are represented as straight lines, because it follows that the factor becomes an additive constant . ${\ displaystyle y = Cx ^ {a}}$ ${\ displaystyle y = Cx ^ {a}}$ ${\ displaystyle \ log (y) = a \ log (x) + \ log (C)}$ ${\ displaystyle C}$ ${\ displaystyle \ log (C)}$

It enables such functions to be drawn easily or to check whether given value pairs match a power function (they must then lie on a straight line). The slope of the straight line is the exponent . ${\ displaystyle a}$

The functions are shown below with the equations and on logarithmic paper. ${\ displaystyle y = x ^ {2}}$ ${\ displaystyle y = x ^ {1/3}}$