Plotting the graph of y=1/log|x|

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To plot the graph of y=1/log|x| efficiently, one can utilize the properties of the logarithmic function and its asymptotes. Analyzing the function's evenness or oddness, identifying roots, and calculating the first and second derivatives can provide insights into its behavior, such as intervals of increase or decrease and concavity. By understanding the graph of y=log|x|, one can infer the shape of y=1/log|x| for both positive and negative x values. Sample points for positive x can help predict the graph's behavior in the negative domain due to the function's symmetry. This approach minimizes the need for extensive calculations while ensuring an accurate representation of the graph.
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I was just wondering as to how I can plot the graph of y=1/log|x| without putting a lot of values of x and obtaining corresponding values of y.
I mean, how can I draw this graph using the graph of y=log x or the graph of log|x|? Is there a way?
 
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There are a lot of tools available to let you help you plot the function. Here are some things you can do:

  • Find the asymptotes.
  • Find out if the function is even/odd/none
  • Find the roots of the function.
  • Find the first derivative and see where the function is increasing/decreasing. Find the extremal points.
  • Find the second derivative and see where to function is concave/convex.

This information will help you make an accurate drawing of the function.
 
IEVaibhov said:
I was just wondering as to how I can plot the graph of y=1/log|x| without putting a lot of values of x and obtaining corresponding values of y.
I mean, how can I draw this graph using the graph of y=log x or the graph of log|x|? Is there a way?

Suppose you work out the graph, using sample points, of the function for positive values of x. Is there some way you would automatically know what the graph looks like for negative values of x?
 

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