When do we use logs

Home Articles Popular Calculus. Feedback Contact About Newsletter. Logarithms are everywhere. Ever use the following phrases? Mama mia! Ok, ok, we get it: what are logarithms about? Logarithms find the cause for an effect, i. By the way, the notion of "cause and effect" is nuanced.

Why is bigger than ? Logarithms put numbers on a human-friendly scale. Logarithms count multiplication as steps Logarithms describe changes in terms of multiplication: in the examples above, each step is 10x bigger. Show me the math Time for the meat: let's see where logarithms show up!

Six-figure salary or 2-digit expense We're describing numbers in terms of their digits, i. Try it out here: Order of magnitude We geeks love this phrase. Interest Rates How do we figure out growth rates? My two favorite interpretations of the natural logarithm ln x , i. Google conveys a lot of information with a very rough scale Measurement Scale: Richter, Decibel, etc.

Logarithmic Graphs You'll often see items plotted on a "log scale". Onward and upward If a concept is well-known but not well-loved, it means we need to build our intuition. In my head: Logarithms find the root cause for an effect see growth, find interest rate They help count multiplications or digits, with the bonus of partial counts k is a 6. Continuous Growth What does an exponent really mean? First I will review what we mean by logarithms. Then I will provide more detail about each of these reasons and give examples.

To refresh your memory of school math, logs are just another way of writing exponential equations, one that allows you to separate the exponent on one side of the equation.

The common base for logarithmic scales is the base However, other bases are also useful. While a base of ten is useful when the data range over several orders of magnitude, a base of two is useful when the data have a smaller range.

Figure 1. Dot plot of revenues of the top 60 Fortune companies. Data Source Figure 1 uses a dot plot to show the revenues of the top 60 companies on the Fortune list which provides revenues for One reason for choosing a dot plot rather than a bar chart is that it is less cluttered. We will be learning other benefits of dot plots in this and future posts. Wal-mart Stores and Exxon-Mobil have much larger revenues than the other companies.

As a result, the differences in the revenues of the other companies are compressed, making these differences more difficult to judge. Figure 2. Dot plot of revenues of top 60 Fortune companies on a log scale with base 2. Next, they also use logs to calculate alterations in atmospheric CO 2 , population growth. Finally, geologists prefer applications of logarithms in radioactive decay-dating estimation, sedimentology, and to determine grain sizes.

When Do We Use Them? What Are Logarithms? There are logarithms using different base units. If you wanted, you could use two as a base unit. In general, you write log followed by the base number as a subscript.