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Graphing Logarithmic Functions

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To create a logarithmic function, you need to devise a set of points and then pull a smooth curve through those points.

To graph, a logarithmic function, follow the step-by-step guide here:

  1. Write the function in logarithmic form. A logarithmic function has the form y = log_a(x), where a is the logarithm base. For instance, the function y = log_2(x) is a logarithmic function with base 2.
  2. Pick a series of values for x and calculate the corresponding values of y. Logarithmic functions are specified only for positive values of x, so you should select a series of x-values that are all positive. For example, you might choose x = 1, x = 2, x = 4, and so on. For each value of x, compute the corresponding value of y using the formula y = log_a(x).
  3. Plan the points on the graph. On the x-axis, plan the values of x that you chose in step 2. On the y-axis, plan the corresponding values of y.
  4. Draw a smooth curve through the points. Logarithmic functions contain a "staircase" shape, with each step depicting the power of the base. To draw the curve, join the points with a smooth curve that follows the general shape of the function.

It is important to remember that the graph of a logarithmic function is always a curve, not a straight line. The curve gets closer and closer to the x-axis as the x gets larger, but it will never touch the x-axis. This is because the values of y in a logarithmic function always approach 0 as x gets larger, but they never really reach 0.

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