Where do you see logarithms?

Written by Adriana Watson, Editorial Writer

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This time of the year, most juniors are exploring the delightful universe of logarithms. It’s one thing to learn how they work for the sake of your test grade, but if you’re anything like me, you might have some questions as to why exactly you need to know that lne=1. And just because I like to be nice sometimes, I’ve constructed a list of 3 interesting ways you can use logarithms in real life. (Warning: If you don’t like the numbers 1 and 0, this may be hard for you.)

1. Google Page Ranking: Google actually uses logarithmic thinking when it comes to ranking pages for you based on popularity and relevance. It does this by more or less saying, “This page is 10x (or 100x…etc) more popular than this one.” In other words, the page with the higher logarithm is ranked higher. For example, a page with log100would be ranked lower than a page with log10000 because the first has a rank of 2 (102=100)while the second has a rank of 4 (104=10000). If you want to get really nerdy, this version is used because it’s easiest to code into the algorithm. The code for this (in simplified Ruby) would look a bit like:

“Website_1” = log(gets.chomp)==”Rank_1”

“Website_2”=log(gets.chomp)==”Rank_2”


if “Rank_1” > “Rank_2”

then prints [“Website_1” , “Website_2”]

else prints [“Website_2”, “Website_1”]

2. Richter, Decibel, and pH Scales: Earthquakes and pH levels also utilize logarithms. PH values are written from a scale of 1-14 which actually derives from the common log of the hydrogen ion concentration. Why is it written in pH (power of Hydrogen) instead of simply moles? Well, which is easier to use: “pH=7” or “hydrogen concentration = 1*107moles”? Logarithms are also used in the Richter and Decibel Scale for the same reasons.

3. Safety Indexing: Ever wondered how they get those “1 in 5 people will…” statistics and translate them to actual safety indexes? Logarithms! For example: 1 in (about) 200,000,000 people die from falling vending machines every year (scary). To get the safety index from this, you would find the common log of 200,000,000 (log200000000),which is about 8.3. What does that mean? The higher the index is, the safer you are. For clarification, the safety index for car crashes is about 3.7, so by comparison, you’re pretty safe from the evils of falling vending machines.

And thus concludes my small list of fabulous things logarithms do. Whether you’re teaching it or learning it, logarithms are actually everywhere. That is, if you know where to look.

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Where do you see logarithms?