# What are the differences between these two methods of Semi-logarithmic plotting?

I have my measurement data in (x, y). I am trying to plot a semi-logarithmic plot of y versus log (x). It looks like that there are two ways to plot such a graph.

1. Transform the values of x to log (x) for all values of x. Then, I could plot (log x, y) similar to that of plotting (x, y).

2. Arrange y in log scale (example, for a base of 10, arrange x axis by a decade), and plot the data set exactly like I would plot (x, y) in this logarithmic scale. In other words, I do not need to compute logarithmic values of x. Instead, I could simply rearrange x axis in logarithmic scale and then plot (x, y).

Here are my two questions:

1. Are both the options discussed above the same thing in terms of data representation? If both methods of plotting are the same, I would assume the slope of data set would be the same using both the methods.

2. I would like to show that my variable in y is linear with log of the variable in x axis. In order to do so, I plotted the (x, y) data set using the second method of plotting discussed above and did a linear fit. I got a R2 value close to 0.95. Please provide comments or your suggestions about the validity of this method.