*36*

A **log-log plot **is a plot that uses logarithmic scales on both the x-axis and the y-axis.

This type of plot is useful for visualizing two variables when the true relationship between them follows some type of power law.

This tutorial explains how to create a log-log plot in Python.

**How to Create a Log-Log Plot in Python**

Suppose we have the following pandas DataFrame:

import pandas as pd import matplotlib.pyplot as plt #create DataFrame df = pd.DataFrame({'x': [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], 'y': [3, 4, 5, 7, 9, 13, 15, 19, 23, 24, 29, 38, 40, 50, 56, 59, 70, 89, 104, 130]}) #create scatterplot plt.scatter(df.x, df.y)

Clearly the relationship between *x* and *y* follows a power law.

The following code shows how to use **numpy.log()** to perform a log transformation on both variables and create a log-log plot to visualize the relationship bewteen them:

import numpy as np #perform log transformation on both x and y xlog = np.log(df.x) ylog = np.log(df.y) #create log-log plot plt.scatter(xlog, ylog)

The x-axis displays the log of x and the y-axis displays the log of y.

Notice how the relationship between log(x) and log(y) is much more linear compared to the previous plot.

Feel free to add a title and axis labels to make the plot easier to interpret:

#create log-log plot with labels plt.scatter(xlog, ylog, color='purple') plt.xlabel('Log(x)') plt.ylabel('Log(y)') plt.title('Log-Log Plot')

Also note that you can create a line plot instead of a scatterplot by simply using **plt.plot()** as follows:

#create log-log line plot plt.plot(xlog, ylog, color='purple') plt.xlabel('Log(x)') plt.ylabel('Log(y)') plt.title('Log-Log Plot')

**Additional Resources**

How to Create a Log-Log Plot in R

How to Create a Log-Log Plot in Excel