Logarithmic Transformation
- Rescales a graph axis using a logarithmic scale to make values easier to compare.
- Helps reveal patterns or trends when data spans a very wide range of values.
- Spreads values more evenly on the axis so details that are hard to see on a linear scale become visible.
Definition
Section titled “Definition”A logarithmic transformation is a way of changing the scale of an axis on a graph.
Explanation
Section titled “Explanation”When plotted on a linear scale, data that covers a very wide range of values can make patterns or trends difficult to see. Applying a logarithmic transformation to an axis changes that axis’s scale so the data are spread out more evenly. This makes it easier to observe details, patterns, or trends that are otherwise obscured on a linear scale.
Examples
Section titled “Examples”Bacteria population growth
Section titled “Bacteria population growth”Imagine that you are a scientist studying the growth of a population of bacteria. You take samples of the bacteria at regular intervals and measure the number of bacteria in each sample. Over time, the number of bacteria grows exponentially, so the data you collect looks like a straight line on a graph when plotted on a linear scale. However, it can be difficult to see the details of this growth when the numbers are so large, so you decide to use a logarithmic scale for the y-axis of your graph. This spreads out the data and makes it easier to see the growth of the bacteria over time.
Stellar brightness
Section titled “Stellar brightness”Imagine that you are an astronomer studying the brightness of a distant star. The brightness of a star is measured in units called magnitudes, and a star with a higher magnitude is dimmer than a star with a lower magnitude. When you plot the brightness of the star on a graph using a linear scale, the data looks like a straight line that slopes downwards. However, using a logarithmic scale for the y-axis of the graph spreads out the data and makes it easier to see how the brightness of the star changes over time.
Use cases
Section titled “Use cases”- Visualizing data that covers a very wide range of values.
- Making patterns or trends easier to see by changing the axis scale.
Related terms
Section titled “Related terms”- Logarithmic scale
- Linear scale