Label the linear x-axis to accommodate the range of values for the independent, x-variable. The range is the difference between the lowest and highest values of the independent variable. For example, if time measurements were taken over a period of 25 seconds, then the range for the x-axis is 25 seconds, starting at 0 s and ending at 25 s. Choose x-axis intervals of 5 s. Start the labeling at 0 s at the origin of the graph and end with 25 s.
Find the power of lowest value for the dependent or y-variable. This power sets the lower limit on the y-axis. For example, if a cell divides into four cells every five seconds, then the cell count will be 1, 4, 16, 64, 256 and 768 at times of 0 s, 5 s, 10 s, 15 s, 20 s and 25 s. The lowest value for the y-variable is 1 = 1 x 10^0. The power of the lowest value is 0.
Label the cycle baselines on the y-axis. The baseline of each cycle is the first horizontal line in each cycle and has the coefficient of 1. The lowest horizontal line on the graph paper is the baseline of the first cycle. You will recognize the baselines of the other cycles as being the last of the closely spaced horizontal lines before which the largest vertical interval occurs. The first baseline bears the power of the lowest y-variable value found in Step 3. For example, if the power of the lowest y-variable value is 0, then the first baseline is labeled as 1 x 10^0. The second baseline is increased by 10 and is labeled as 1 x 10^1. The third baseline is again increased by 10 and is labeled as 1 x 10^2.
Label the remaining horizontal lines on the y-axis. Keep the same power of 10 as for the baseline of each cycle, but increase the coefficient by 1 from one line to the next. For example, if the three baselines of the three-cycle semi-log paper are labeled as 1 x 10^0, 1 x 10^1 and 1 x 10^2, then the eight lines between the first and second baseline will be 2 x 10^0, 3 x 10^0, 4 x 10^0, 5 x 10^0, 6 x 10^0, 7 x 10^0, 8 x 10^0 and 9 x 10^0. The eight lines between the second and the third baselines will be 2 x 10^1, 3 x 10^1, 4 x 10^1, 5 x 10^1, 6 x 10^1, 7 x 10^1, 8 x 10^1 and 9 x 10^1. The top eight lines of the third cycle are 2 x 10^2, 3 x 10^2, 4 x 10^2, 5 x 10^2, 6 x 10^2, 7 x 10^2, 8 x 10^2 and 9 x 10^2.