How to graph information on semi-log graph paper

Written by pearl lewis
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Semi-log graph paper combines a logarithmic scale with a linear scale. This paper allows you to graph exponential values without having to first do any logarithmic calculations. The linear x-axis of semi-log paper has equally spaced intervals. The logarithmic y-axis consists of cycles. Each cycle is divided into non-uniform intervals, and is labelled from 1 to 9. Each cycle represents a factor of ten increase equivalent to shifting the decimal point by one space to the right. You can use semi-log paper to graph data that exhibits exponential or rapidly changing trends.

Skill level:
Moderately Challenging

• Pencil
• Ruler

Instructions

1. 1

Label the x-axis with the name of the independent variable. For example, if graphing the size of a virus sample as a function of time, time would be the independent variable.

2. 2

Divide the x-axis into intervals that accommodate the full range of x-variable data. The range includes all the x-variable values from the lowest to the highest. For example, if the virus sample was allowed to grow for 5 minutes, then the x-axis could need to accommodate times ranging from 0 to 5 minutes. Divide the axis into 5 equally spaced 1 minute intervals starting with t = 0 at the graph origin, and ending with t = 5 min after the fifth time interval.

3. 3

Label the y-axis with the name of the dependent variable. For example, if graphing the size of a virus sample as a function of time, size would be the dependent variable. The size of the virus sample increases as time passes, so the sample size is dependent on the time.

4. 4

Label the y-axis to accommodate the range of y-variable data. Label the first logarithmic cycle so that it includes the first data point. For example, if the size of the virus sample is 5 units at the start the experiment, then the first cycle must include the number 5. Label the scale ticks in the first cycle starting with 1x10^0 and ending with 9x10^0. The second cycle is labelled with 1x10^1 to 9x10^1. Keep increasing the labels on each subsequent cycle by a factor of 10. Choose the appropriate type of semi-log paper based on the range of your dependent variable. Semi-log paper is available in a variety of cycle sizes, and is labelled according to the number of cycles. For example, one-cycle semi-log paper only includes one complete logarithmic cycle, while seven-cycle paper has seven cycles.

5. 5

Plot each data point on the semi-log paper. Each data point consists of an x-variable and a y-variable. Find the x-value of the data point on the x-axis. Find the corresponding y-variable value on the y-axis. Follow the vertical line from the x-value on the x-axis to where the vertical line crosses a horizontal line originating at the y-value on the y-axis. Place a pencil dot on the graph where the horizontal and vertical lines intersect. This dot represents the data point.

6. 6

Find the best-fit line through all the data points. (See Resources 1, 2, 3) Use the ruler to draw a line through the data points. Do not join the dots. A best-fit line is the straight line that best represents the data points.

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