Log-Log graphs are often used to determine the relationship between variables in an equation. If the dependent variable is proportional to a power of an independent variable then the graph of the dependent variable as a function of that independent variable with all other variables held constant will be a straight line when plotted on a Log-Log graph. The slope of the line will be the power. The slope of the line for y = x will be +1 decade/decade when plotted on a log-log graph as shown below.
The function y1 is y = x. Its graph rises one decade for each decade increase in x. The function y2 is y = x2 Its graph has a slope of +2 decades rise for each increase of one decade in x. A graph of the function y = x -3/2 would have a slope of -3/2 decades per decade.
Log-Log graphs can be plotted by right clicking on the desired axis,. then selecting format axis or axis properties from the dropdown menu. Then clicking on log scale. The grid lines can be turned on in Excel by selecting chart from the menu. Then click on chart options. Then select gridlines. Then check the gridlines you want turned on. In QuatroPro select the axis and right click on it. Then select axis properties. Then select major or minor grid and set the desired properties. I recommend using solid lines for the major grids and dashed lines for the minor grid lines. For printing purposes I recommend selecting black as the color for the grid lines. Actually I recommend that the entire graph be printed in black. Different curves can be identified by using different line types.
Creating Log-Log graphs in Excel
Create a graph in the normal manner. Right Click on the X-axis. This will bring up a menu that allows you to select Format Axis. In the Format Axis window select the Scale tab. Then check the box labeled Logarithmic scale. Do the same thing for the Y-Axis. Set the crossing point of each axis at the minimum value of the other axis.
When the graph is selected, The item "Chart" will appear in the menu at the top of the screen. Click on Chart. Then click on Chart Options from the dropdown menu.
In the Chart options window select Gridlines. Then turn on both Major and Minor grid lines for both axes. Then right click on one of the minor grid lines and select Format Gridlines. In the format Gridlines window, change the line style to dashed line. If the color is not black change it also. Most graphs print better using black lines.
Right click in an open part of the plot area and select Format Plot Area from the drop down menu. Then change the Area color to none. This saves on printer ink as well as making the graph easier to read.
Also on the format axis menu under scale the position at which the other axis crosses this axis can be specified. This should usually be set so that the x axis scale is at the bottom of the y axis and the y axis scale is at the left end of the x axis. Therefore set the crossing value to the minimum value and check the Value () axis Crosses at: box.
