Logarithmic Scale

Definition

Logarithmic Scale

In a Cartesian coordinate system, sometimes, one or more axes are log-scaled, meaning that the points are logarithmically aligned.

Values

Negative Values

Since is not defined for negative values, log-scaled axes can only represent positive values.

, which is equal to 1, is the -line which is why negative values cannot be .

Values between 0 and 1

However, values between (0 and 1 excluded) are represented in the -line:

Values between Integers

Example: The difference is smaller than . Therefore, the log-values are not equidistant.

Log-Scale for Y:

Log-Scale for X:

Types

X Axis only

Logarithm functions appear as a straight line in a -log coordinate system.

Y Axis only

In a -log coordinate system, exponential functions are represented as straight lines.

Why is it a Straight Line?

Applying the logarithm to an exponential function :

Let and , the equation can be formulated as:

Which is a linear function. Therefore, -logscaled exponential functions are linear functions.

Both axes: X and Y

Power functions appear as a straight line in -logscaled coordinate systems.