Understanding Linear-Log Plots & Their Uses

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A linear-log plot is a graphical representation where one axis is linear and the other is logarithmic, commonly used to analyze data that follows an exponential distribution. This type of plot allows for easier visualization of relationships between variables, particularly when data points align closely with a logarithmic curve. By transforming the x-axis to a logarithmic scale, data that fits the form y = A log(x) + B can be represented as a straight line, simplifying the identification of trends. This method is advantageous because it facilitates the application of standard formulas for determining the best fit line, making it easier to assess the fit of empirical data against theoretical models. Overall, linear-log plots are valuable tools for analyzing and interpreting exponential relationships in data.
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What is meant by a linear-log plot and why is it used?

In the book I have, the author is demonstrating that some data fits an exponential distribution. So what he does is a linear-log plot of both the exponential distribution and the empirical data, and then overlaps the 2 graphs so show they follow a similar path.

So my question is, what exactly is a linear-log plot, and when/why do you use it?
For exmaple, if I was to show the data fitted an exponential distribution, I would just plot the data and exponetial distribution as they were, and overlap them and show they fit (or don't fit).
 
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If you have data that happens to lie close to a curve of the form y= A log(x)+ B, (conversely, x= e^{\frac{y-B}{A}) then Plotting y against "X= log(x)" rather than x itself puts the points close to the straight line y= AX+ B. Yes, you could overlap your raw data and an exponential (if you were sure of the constants involved) and show that they matched but it is typically much easier to spot a straight line than more complex curves and there are standard formulae for the "best fit" line.
 
First trick I learned this one a long time ago and have used it to entertain and amuse young kids. Ask your friend to write down a three-digit number without showing it to you. Then ask him or her to rearrange the digits to form a new three-digit number. After that, write whichever is the larger number above the other number, and then subtract the smaller from the larger, making sure that you don't see any of the numbers. Then ask the young "victim" to tell you any two of the digits of the...

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