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 R using both base R and the data visualization package .

**Method 1: Create a Log-Log Plot in Base R**

Suppose we have the following dataset in R:

#create data df <- data.frame(x=3:22, y=c(3, 4, 5, 7, 9, 13, 15, 19, 23, 24, 29, 38, 40, 50, 56, 59, 70, 89, 104, 130)) #create scatterplot of x vs. y plot(df$x, df$y, main='Raw Data')

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

The following code shows how to create a log-log plot for these two variables in base R:

#create log-log plot of x vs. y plot(log(df$x), log(df$y), main='Log-Log Plot')

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

**Method 2: Create a Log-Log Plot in ggplot2**

The following code shows how to create a log-log plot for the exact same dataset using ggplot2:

library(ggplot2) #create data df <- data.frame(x=3:22, y=c(3, 4, 5, 7, 9, 13, 15, 19, 23, 24, 29, 38, 40, 50, 56, 59, 70, 89, 104, 130)) #define new data frame df_log <- data.frame(x=log(df$x), y=log(df$y)) #create scatterplot using ggplot2 ggplot(df_log, aes(x=x, y=y)) + geom_point()

Feel free to customize the title, axis labels, and theme to make the plot more aesthetically pleasing:

ggplot(df_log, aes(x=x, y=y)) + geom_point() + labs(title='Log-Log Plot', x='Log(x)', y='Log(y)') + theme_minimal()