SEMI-LOG GRAPHS A graph in which the y-axis (the ordinate) has a logarithmic scale and the x-axis (the abscissa) has an arithmetic scale is known as a semi-log graph. Semi-log graphs are commonly used in many diverse fields, including engineering, chemistry, physics, biology, and economics.

SEMI-LOG GRAPHS Note the nonuniform spacing of the units along the logarithmic scale. Also, note that the location of 1 on the logarithmic scale is equivalent to the location of log 1 on the arithmetic scale (because log 1 = 0, as shown on the arithmetic scale). Similarly, the location of 2 on the logarithmic scale is equivalent to the location of log 2 on the arithmetic scale (because log 2 = 0.30), and so on. Thus, we see that plotting x (or y) on a logarithmic scale is equivalent to plotting log x (or log y) on an arithmetic scale. Note that you simply plot the value of x (or y) directly when plotting data on a logarithmic scale. You need not calculate the log of x (or the log of y)—the logarithmic scale automatically does this for you.

Example 5.4 Creating a Semi-Log Graph in Excel Convert the arithmetic x-y graph developed in Example 5.1 and shown in Fig. 5.13 into a semi-log graph. The voltage drop across a capacitor varies with time in accordance with the formula 𝑉 = 10 𝑒 −0.5𝑡 where V represents voltage drop, in volts, and t represents time, in seconds. Prepare an x-y graph of the voltage as the time varies from 0 to 10 seconds. Display the data to three-decimal precision using arithmetic coordinates. Label the graph so that it is legible and attractive.

LOG-LOG GRAPHS A log-log graph has logarithmic coordinates along both axes. Thus, it is equivalent to a plot of log y against log x using arithmetic coordinates. Log-log graphs are useful for plotting scientific and technical data because they allow the data to span several orders of magnitude and because a power equation of the form 𝑦 = 𝑎 𝑥 𝑏 will appear as a straight line.

Example 5.5 Creating a Log-Log Graph in Excel Create a log-log graph of the area and volume of a sphere as a function of the radius within the interval 0 ≤ r ≤ 10, using the following two formulas. 𝐴=4𝜋 𝑟 2 and 𝑉= 4 3 𝜋 𝑟 3

LINE GRAPHS Line graphs, unlike x-y graphs, are used to represent single-valued (categorical) data. Usually, the data points represent different values of the same entity, such as the average daily temperature for each of several consecutive days. Do not confuse x-y graphs (called XY Charts or Scatter Charts in Excel) with line graphs (called Line Charts in Excel). If the independent variable varies continuously (e.g., time or distance), you should always use an x-y graph rather than a line graph to represent the data.

Example 5.6 Creating a Line Graph in Excel

BAR GRAPHS (EXCEL COLUMN CHARTS) A bar graph, like a line graph, is used to represent single-valued (categorical) data. Unlike a line graph, however, a bar graph utilizes a series of vertical rectangles (bars) to represent the data.

PIE CHARTS A pie chart shows the distribution of individual data items within a data set. Like line graphs and bar graphs, pie charts represent single- valued data.

An aluminum alloy has the following chemical composition: Element Weight (percent) Aluminum (Al) 93.25 Chromium (Cr) 0.5 Magnesium (Mg) 0.6 Titanium (Ti) 0.15 Zinc (Zn) 5.5 Enter the data in an Excel worksheet and create a bar graph and a pie chart showing the composition. Include appropriate labels and a title. Arrange the objects so that the graph is attractive.