Content

• To step
• Method 1 of 2: Read the axes of the graph
• Warnings

Most people are familiar with reading numbers on a number line or reading data from a graph. However, a standard scale is not useful under certain circumstances. If the data is growing or decreasing exponentially, then you have to use what is called a logarithmic scale. A graph of, for example, the number of McDonald's burgers sold over time would start at 1 million in 1955; than 5 million just a year later, then 400 million, 1 billion (in less than 10 years) and up to 80 billion in 1990. This data would be too much for a standard graph, but can easily be represented on a logarithmic scale. Know that a logarithmic scale has a different system for representing numbers, which are not evenly spaced like on a standard scale. By knowing how to read a logarithmic scale, you can read the data more effectively and display it graphically.

To step

Method 1 of 2: Read the axes of the graph

1. Determine whether one or both axes use a log scale. Charts showing rapidly growing data can use axes with one or two log scales. The difference is whether both the x and y axes use logarithmic scales, or just one. The choice depends on how much detail you want to display with the graph. If numbers on one axis or the other are growing or decreasing exponentially, you may want to use a logarithmic scale for that axis.
   • A logarithmic (or just "log") scale has irregular grid lines. A standard scale has evenly spaced grid lines. Some data should only be drawn on standard paper, some on semi-log charts, and some on log-log charts.
   • For example: The graph of ${ displaystyle y = { sqrt {x}}}$Read the scale of the main classification. On a logarithmic scale chart, the evenly spaced markers represent the powers of the base you are working with. The standard logs use either the base 10 or the natural log with ${ displaystyle e}$Note that small intervals are not evenly spaced. If you are using logarithmic graph paper, you will notice that the intervals between the main devices are not evenly spaced. That is, for example, the mark for 20 would actually be placed about 1/3 the distance between 10 and 100.
     • The minor intervals are based on the logarithm of each number. So if 10 is represented as the first major mark on the scale and 100 as the second, then the other numbers fall in between as follows:
       • ${ displaystyle log (10) = 1}$Determine the type of scale you want to use. For the explanation below, the focus will be on a semi-log graph, using a standard scale for the x-axis and a log scale for the y-axis. However, you may want to reverse these depending on how you want to view the data. Reversing the axes causes the graph to shift ninety degrees and can make the data easier to interpret in one direction or the other. In addition, you may be able to use a log scale to spread out certain data values ​​and make their details more visible.
       • Mark the scale of the x axis. The x axis is the independent variable. The independent variable is the variable that you generally control in a measurement or experiment. The independent variable is not affected by the other variable in the study. Some examples of independent variables are:
         • Date
         • Time
         • Age
         • Medication given
       • Determine that you need a logarithmic scale for the y axis. You will use a logarithmic scale to map data that is changing extremely quickly. A standard chart is useful for data that is growing or falling in a linear fashion. A logarithmic graph is for data that changes exponentially. Examples of such data are:
         • Population growth
         • Consumption
         • Compound interest
       • Label the logarithmic scale. Review your data and decide how to mark the y axis. If your data only measures numbers within the millions and billions, for example, then you probably don't need to start the graph from zero. You can label the lowest cycle on the chart as ${ displaystyle 10 ^ {6}}$Find the position on the x axis for a data point. To graph the first (or any) data point, start by locating its position along the x axis. This can be an ascending scale, such as a regular number line 1, 2, 3, etc. It can be a scale of labels that you assign, such as dates or months of the year in which you take certain measurements.
       • Find the position along the logarithmic y axis. You need to find the corresponding position along the y axis for the data you want to plot. Remember, since you are working with a logarithmic scale, the major markers are powers of 10 and the minor scale markers between them are the subdivisions. For example: between ${ displaystyle 10 ^ {6}}$Continue with all data. Continue repeating the previous steps for all the data you need to create a chart. For each data point, find its position along the x-axis first, and then find its corresponding position along the logarithmic scale of the y-axis.

Warnings

• If you are reading data from a logarithmic scale, make sure you know which base is used for the logarithm. Data measured in the base 10 will be very different from data measured on a natural log scale with base e.