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(Describer) Titles: NM State University Learning Games Lab. A pencil writes the word "Presents."

(Describer) Finding Your Place on the Scale.

(Describer) An animated girl wearing glasses walks.

(narrator) Logarithms. The word itself has a magnitude that has caused even the most decorated veterans of soil studies to break down and weep. Don't worry. They're fine now. In reality, there is nothing to fear about logs. We must simply learn to understand them. Soil science uses the logarithmic scale to predict how much water is available to plants. Let's start with a scale you're familiar with, a linear scale, like the one used to measure distance on a globe. The notches on a linear scale are evenly spaced. On this scale, each notch indicates an increase of 200 units. Perhaps the most basic of linear scales is a scale of 1 to 10, the go-to rating for measuring anything from the quality of a film to the attractiveness of another person.

[narrator purrs] Arrr-wow!

This scale works just like we expect. The number 5 sits exactly between 0 and 10, with the other numbers evenly spaced in between. Linear scales, such as this one, are additive, which means we add a value to increase or decrease on the scale. Logarithmic scales are multiplicative or exponential. That means we multiply a value to increase on the scale. So, on a linear scale, we add: 0 plus 1 is 1... plus 1 is 2... plus 1 is 3. And on a logarithmic scale, we use exponents: 10 to the power of 1 is 10; 10 times 10 is 100; 10 to the power of 3 is 1000. But why should we use the log scale? Why not just use the linear scale to measure things? Picture an astronaut's house. Now, think about the distance the astronaut drives from the house to the launchpad. This distance is tiny compared to the distance that the astronaut's rocket travels to the moon. And the distance to the moon is just a small hop compared to the distance to the sun. If all of these points were placed on a linear scale, that scale would be very hard to read since the data is extremely spread out for large values but really close for small values. A log scale solves this problem by expanding the small values of data where the points are tight and compacting all of the large values where data is spread out. At first glance, the log scale could be confused with a linear scale. The notches are evenly spaced. But don't forget that, although there is an even distance between numbers marked on the scale, they are actually increasing quite rapidly... well, exponentially. You see, this group has a total of 9 numbers, while this has 90, and this one has 900. Each group has 10 times the last. Now let's take a look at this space. The numbers in here don't appear like they do in a linear scale. Instead, they start far apart and get closer together as they increase in value. This is how we visually compress all our data. There are many systems that use logarithms: the galactic scale, the microscopic scale, the decibel scale, photographic f-stops, the Richter scale, and even soil particle size, which we'll look at next. All of these graph information that is measured exponentially. This graph shows us the particle surface area in relation to the particle size. The y-axis measures the specific surface area of each particle. The x-axis keeps track of particle size, expressed as a particle's diameter or width. As the y-axis increases by 50,000 with each notch, the x-axis starts at 1 10,000th and increases by a factor of 10 with each notch, which means we multiply each notch by 10. And we know multiplicative means logarithmic. So, particle size on the x-axis is logarithmic. This set of data is already plotted for us. We can see it on this curve. To find the values at any point on the curve, we simply draw a line from the curve to each axis. Let's find the particle surface area and size for this point on the curve. We'll make a line to the y-axis to find the surface area. That's about 75,000 millimeters squared per gram. Now we make a line to the x-axis for the particle size. Remember, this is not a linear scale. It is logarithmic. So, instead of evenly spaced notches, the notches compress to the right. We see the compression of 2, 3, and 4 10,000ths, all the way up to 0.001. It appears that the particle size for our sample is 5 10,000ths of a millimeter wide. You can find the exact position of these values by using a calculator. But when estimating, all you need to know is this pattern and how they are compressed to the one side. And that's all there is to it. Now you can fearlessly tackle a logarithmic scale representing any set of data. See, although they may be intimidating at first, logs are actually helping us. Aren't you, little log?

(Describer) A book called "I heart logs" leaps into the animated girl's arms. Behind her, a banner above soil scientists reads, "congrats!"

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(Describer) Titles. Additional materials available at ScienceOfSoil.org.

(Describer) Executive producer Dr Jeanne Gleason. Project directors Dr. Barbara Chamberlin. Dr. Jeanne Gleason. Dr. April Ulrey. Production management Pamela N. Martinez.

(Describer) Project management Seth Powers. Elizabeth Sohn. Content Expertise Dr. April Ulrey. Dr Erica Vogues. Instructional design and script. Dr Barbara Chamberlin. Pamela N Martinez. Seth Powers. Amy Smith. Art and Animation Stephen Dye. Seth Powers. Vocal talent Eric Young. Special thanks to NMSU Learning Games Lab Consultants and participating NMSU faculty and students. Accessibility provided by the US Department of Education.

Accessibility provided by the U.S. Department of Education.

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