Using search engine logarithmic scales

[hof]

Hi there,

I have a problem for work that is stirring up lots of memories of University Math courses, and I need help!

I work in search engine optimization, and search engines use logarithmic scales to value pages and websites. I'm using a tool that mimics those scales and assigns a number between 1 and 100 to the value and importance of a page on the internet. I understand that the difference between a page with 'pagerank' 4 has 10x the value of a pr 3. But this particular tool breaks it into fractions, so I'm trying to compare for example a page with PR 34 and a page with PR 41. How can I create a fixed number that better represents the relative importance?

Also, there are two logarithmic 'scores' given, one for the page (PR) and one for the domain (DR). Does anyone have any suggestions for how to combine the two into a single number that could be compared against a second 'set'. For example, page A has a PR 34 and DR 55, compared with page B with a PR 30 and DR 58. I'm going to assume both scores are weighted equally.

Thanks for the help! I can't quite wrap my head around it.

Mike

 

[jvicens]

Hi Mike,

It's great to see that you are using logarithmic scales to measure the value and importance of web pages in search engine optimization. Logarithmic scales are commonly used in various fields of science and mathematics, as they allow us to better represent and compare data that varies greatly in magnitude. In your case, the logarithmic scale is being used to represent the complex and ever-changing world of the internet.

To better understand how to create a fixed number that represents the relative importance of two pages with different pagerank scores, let's first review how logarithmic scales work. As you mentioned, the difference between a page with PR 4 and PR 3 is 10x. This is because logarithms are the inverse of exponential functions. On a logarithmic scale, each increase of 1 represents a 10x increase in the original value. So, a page with PR 4 has a value 10 times greater than a page with PR 3. Similarly, a page with PR 5 has a value 10 times greater than a page with PR 4, and so on.

Now, to compare two pages with different pagerank scores, you can use the formula log(x/y) = log(x) - log(y), where x and y represent the pagerank scores of the two pages. This will give you a fixed number that represents the relative importance of the two pages. For example, using your example of pages with PR 34 and PR 41, the formula would be log(41/34) = log(41) - log(34) = 1.11394 - 1.53148 = -0.41754. This means that the page with PR 41 has a value 0.41754 times greater than the page with PR 34. You can use this formula for any two pages with different pagerank scores to get a fixed number that represents their relative importance.

As for combining the two logarithmic scores (PR and DR) into a single number, you can use a weighted average formula. This will allow you to give more importance to one score over the other, depending on your needs. For example, if you want to give equal weight to both scores, you can use the formula (PR + DR)/2. This will give you a single number that represents the combined importance of the page and the domain. You can then compare this number with another combined score to determine which page is more important