when you're graphing a log graph what are is the counting pattern?
Look at the log-log graph on this page:
http://www.squarecirclez.com/blog/zipf-distributions-log-log-graphs-and-site-statistics/702
On your paper, you will see between the 10, 100, 1000 scales other lines. These are cardnial equivalents to (between the 10 and 100 for example)20, 30, 40, 50, ...
http://en.wikipedia.org/wiki/Logarithmic_scale
see the log scales on that link, and on this may help you.
http://www.physics.uoguelph.ca/tutorials/GLP/
When graphing a logarithmic function, the counting pattern refers to the intervals along the x-axis where you evaluate the function and plot the corresponding points on the graph. The counting pattern for a logarithmic graph depends on the base of the logarithm.
Here's the step-by-step process to determine the counting pattern for a logarithmic graph:
1. Determine the domain: Identify the permissible values for x in the logarithmic function. The domain of a logarithmic function excludes any values of x that result in a negative or zero result when plugged into the logarithmic expression.
2. Find the intercepts: Determine the x and y-intercepts by evaluating the logarithmic function when x equals zero and when y equals zero.
3. Identify symmetry (optional): Some logarithmic functions have symmetry properties, which means that certain points on one side of the y-axis have a corresponding point on the other side. If symmetry exists, identify those points as part of the counting pattern.
4. Choose a base: Logarithmic functions can have different bases, such as base 10 (common logarithm) or base e (natural logarithm). The base determines the shape of the graph, but the steps remain the same regardless of the base.
5. Select values for x: Choose specific values of x within the domain and evaluate the logarithmic function for each value. For example, you can choose x = -2, -1, 0, 1, 2. Note that you can also select values greater than 2 and less than -2 to explore the behavior of the function outside the visible range on the graph.
6. Calculate corresponding y-values: Plug each selected x-value into the logarithmic function, and compute the corresponding y-value or logarithm of that x-value.
7. Plot the points: Once you have the x and y-values, plot each point on the graph.
8. Observe the pattern: Look at the points you have plotted and observe the pattern they form. Depending on the base, logarithmic graphs usually exhibit distinct characteristics like a vertical asymptote, horizontal asymptote, increasing or decreasing behavior, or concavity.
By following these steps, you can determine the counting pattern and accurately graph a logarithmic function.