Hi Kalid,
Enjoyed this very informative post. Can you also write about electricity voltage, current etc.
Nilesh Joglekar
Thanks David, happy to hear it clicked.
100 increases to $150 in 5 years. What is the yearly interest rate? I got 5√150/100=8.45%. and when working it out logically, that’s the right answer. How did you get ln (150/100) /5=8.12%?
Thanks for this post. I’m trying to understand how Moz Domain Authority (DA) works. They say DA is measured on a 100-point logarithmic scale.
Does that mean DA30 is 10x more powerful than DA20?
OR
Is DA21 10x more powerful than DA20, and DA30 would then be… 10^10x (100 million times)?
OR
Is it base-2 not base-10 and DA21 is 2x more powerful than DA20, but DA30 would be 1024x more powerful than DA20…
Help?!?! 
Thanks,
Josh
@Andrew: Great question. 8.45% is the yearly interest rate, assuming we compound every year. 8.12% is the yearly interest rate if we assume we can compound continuously.
If we compound continuously, we’ll end up with 8.45% at the end of each, but an individual dollar only expects to gain 8.12%. It’s the “interest that interest years” that boosts the rate up to 8.45%. e and natural log deal with the perspective of what an individual dollar thinks it is earning. There’s more here: http://betterexplained.com/articles/think-with-exponents/
@Josh: Good question. 100-point logarithmic scale could be setup in any way, but I’m assuming they mean base 10, and that every 10 points means 10x more powerful.
(Having every point be 10x more powerful isn’t necessary, since 10^100, the max of the scale, is an enormous number. Also, having a base 2 scale isn’t that human friendly.)
In this case, every 10 points would be a 10x increase in importance (10, 20, 30, 40, 50) would be (10, 100, 1000, 10k, 100k).
Just my guess but that’s similar to how page rank works (except it’s a 1-10 scale vs 1 to 100, so 1, 2, 3, 4, 5 is 10, 100, 1000, 10k, 100k).
logerthems are very tuff
Thanks, Kalid! 
Very helpful information for my project
awesome,…
helpfull man,…
thanx for share
Thank you so much, this was very useful.
Richter’s scale does NOT end at 10, but there just have never been any earthquake with higher magnitude. (I think that even magnitude 10 was not reached.)
@Ondřej: Good clarification, updated the post.
Hm
Hi Kalid!
So far, your explanations have been helping me out the best I’ve always struggled with math and I can’t even begin to tell you how grateful I am for this site.
I have a “blurry” idea of how logs find the input of growth vs the output, but I think if I read if over again a few more times it should become a little clearer. My biggest struggle right now though is looking at log-transformations in terms of normal distributions/bell curves. On the graph you show here the x axis is time/years but on the graphs I usually see there are negative and positive numbers. I read your other article about how a ln(fraction) is negative because it is the amount of time for something to halve when the model assumes growing forward, but is it the same for logs?
Aha!
Many thanks for this
Thanks for the real explanation. I think this is the way our teachers should teach us.
Too good Kalid. I now understand the importance of Log in real life better. Will be easier to teach my kids.
Hi Ben, thanks for the feedback! I reworded that section.
Love these articles and the intuitive explanations they give, but a bit of criticism on the computer memory section. 16 extra bits of memory is just that, 16 extra bits. When someone says they’ve moved from a 16 bit to a 32 bit system, they’re typically referring to word length (so length of instructions and data, well in a Von Neumann system anyways). What this means is that addresses are now 16 bits longer, so you can refer to 65536 times as many places in memory (each of which most likely contains a word itself, hence the whole 4GB RAM limit you used to see on 32 bit OSes).
What you should instead refer to is the number of possible values a 16 bit number can assume vs a 32 bit number. (And you could do this visually using smaller numbers, like 2 and 3 bits).
You probably understand this, but I think the section could use some rewording for clarity, particularly the last sentence.
Actually thinking about it a bit more, the 4GB would imply the memory is byte and not word addressable (~4 billion addresses (2^32), each 1 byte = 4GB).
Thanks for the post, it was really helpful =)