Friday, March 20, 2009
Logarithms
One application of logarithms is the Richter scale. "The Richter earthquake scale was developed in 1935 by Charles Richter in order to define the relative size and strengths of earthquakes."(UCL 2003) Aside from the Richter scale, what are other ways that logarithms have been used in the real world? Perform a google search and find a valid source that gives a description of another use for logarithms. Write 5-7 sentences describing the use and your opinion about it.
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Logarithms are used in physics, mathematics and engineering. Radioactive decay, bacterial and population growth all involve the use of logarithms. They make division and multiplication easier with extremely large functions. (Ask Dr. Math - http://mathforum.org/library/drmath/view/66629.html)
I think logarithms are stupid. There will be no need that I will have to use these ridiculous functions outside of a math class. The only way I even understand how to do these functions is with a calculator. I will also not be studying the growth of bacteria or a population and therefore will not be using logs. Also, radioactive decay does not interest me, nor does the mathematical equation to decide how quickly it appeared. Natural logs have even less of a chance of being used in my lifetime outside of the classroom.
After learning about the use of logarithms in the Richter Scale, I googled "logarithms" +real world and found a website written by a math teacher. She said the logarithms were used to measure sound waves, or decibels. I was pretty surprised to learn this, becasue the wave that waves move I assumed decibels would be measured using trig functions, although they can be trig functions using logarithms. While I don't see myself ever going into a field that will require me to use logarithms to measure sound waves I found this information useful becuase I love listening to a playing music, so decibels play a pretty large role in my life. Hopefully someday if I'm on Jeopardy this will be the Final Jeopardy question and I will wager everything and win, all thanks to today's class.
http://mathcentral.uregina.ca/QQ/database/QQ.09.00/musgrove1.html
Apparently, logarithms can be used to determine the rate of melting of glaciers. "The simplest, and possibly most elegant, treatment of
sensible-heat flux assumes that both wind speed and
temperature increase as the natural logarithm of the height above the surface, i.e. the so-called logarithmic profile for a neutral boundary layer" (http://www.igsoc.org/annals/50/50/a50a021.pdf). I think this application is really useful. It is kind of hard to stare at a glacier and figure out how quickly (or slowly) it is melting,so using logarithms would simplify the process by predicting a rate of change. Moreover, this application would go a long way in the study of global warming, a serious problem in our world today. If we could effectively use logarithms to analyze the rate of melting of glaciers, we could infer the effect that global warming is having on this planet and take the appropriate steps to control this problem.
http://www.sosmath.com/algebra/logs/log5/log5.html
This website shows people a few applications of logs in everyday life, such as populations, mortgage problems, earthquake problems (obviously), radioactive decay problems, and interest rate problems. I'm going to look into the radioactive decay application, written by Nancy Marcus.
"Example 1: If you start a biology experiment with 5,000,000 cells and 45% of the cells are dying every minute, how long will it take to have less than 1,000 cells?" (Marcus)
Marcus guides the students through the problem instead of just ignoring them to figure it out themselves by laying out a 'math map' of sorts. She explains that one has to go about the issue in steps, and eventually has to utilize the natural log, because the number e has been used in her equation (Marcus). Using the natural log function, Marcus simplifies the equation down to the solution: f(t) = 5,000,000 x e^-.597837(t). Interesting.
Another application of the logarithmic function is population, like I already said. Again, Marcus uses the natural log function because the population expansion is exponential (Marcus).
It seems that the most useful application of logs in life is when dealing with problems which involve exponential growth or decay.
Website used: http://www.sosmath.com/algebra/logs/log5/log5.html
Both/ all articles written by Nancy Marcus.
Logarithms can be used in finding radioactive decay in objects. Substances decompose according to a formula A=A0ekt where t is time and k<0. This formula gets the half-life of radioactivity in objects. This means that it is the amount of time for half the radioactivity to go away. After some work, including taking the natural log of both sides, you come up with the half-life of the ojbect in question. http://math.usask.ca/emr/examples/expdeceg.html
This method seemed a lot harder than what we do in class so I do not think we should try to find the half-life of something.
logarithms can be used in many fields of study. These can include Mathmatical study, geological measurements, and physics calculations. Similar to logarithms used in the richter scale, they are also used in measuring sound levels or decibels. An eqation used to measure decibels is "Lp = 20 log(p / p0) = 10 log(p2 / p02)" (http://hep.physics.indiana.edu/~rickv/Sound_Pressure_Level.html). Logarithms are used for many studies which i am not exactly interested in. I find them slightly interesting. Sopmetimes i find myself wondering in class," who comes up with this stuff." All in all i think logarithms are stupid and that i have no use for them.
Not only are Logarithms used in association with the Richter Scale, but is also used in dealing with the pH scale and finding sound decibels. Also, astronomers and astronauts would have to endlessly deal with numbers of such an incredibly quantity without logarithms. Logarithms simplify their naturally harder work by being used as their axes for their graphs and charts. Also, banking and investment values are often based off of semi-log scales. Other places include population growth (in association with biology), anthropology (carbon dating) and finance (compound interest). Logarithms are used more often than we believe in the real world, and they offer us differing ways to solving problems not only in Calculus, but in normal everyday life.
http://answers.yahoo.com/question/index?qid=20070501092613AAeBRpP
http://videos.howstuffworks.com/hsw/19978-math-factor-the-real-world-and-logarithms-video.htm
The pH scale is the other use of Logarithms in real life. In Chemistry , we use the pH scale to determine the acidity or alkalinity of a solution.The scale ranges from 1 to 14, with 1 being the most acidic and 14 the most alkaline.
Logs are useful in lots of area, especially in Chemistry. There are many situation that I need to use the log method to solve whatever I was working on. It sometimes confuses me with natural log (In)and e. I still don't get the concept of what is a log.
Along with the Richter scale, another real world scale used that involves logarithms is the scale that is used to measure the loudness of sound in decibels. Logarithms are also used in the pH scale, which is used to measure acidity. As such, they stretch out the scale where the acidity or loudness is weak (and small variations noticeable) and compress it where it is strong (where big variations are needed for a noticeable effect). There are many things that are used in today's world that would not be able to be done without logarithms. These two important things, along with many others, are the way they are because of the use of logarithms to figure them out.
Logarithms were created by Joost Burgi. After learning about logarithms in class I realized that they can also be used in the real world. Logarithms are used in many ways to measure physical quantities. They are often used in measureing earthquakes but can also be used in measuring growth and radioactive decay. Some people even use logarithms to study the rate of melting glaciers.(Math Central). I think that logarithms are not used often in the real world but they can be of some importance.
Evan Basile
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There are many different ways in which logarithms are used in everyday life. In chemistry the acidity of a solution is measured using the pH scale. The scale measures the concentration of hydrogen on a scale of 1-14. Each point is ten times more basic than the previous. For example sea water whose measure is 8 is sixty times more basic than lemon juice which is measured 2 on the scale. The unit bel, named after Alexander Graham Bell is uses base-10 logarithm to show ratios of voltage levels and power levels. This unit is used mostly in telecommunications and electronics.
Is there a new car you are interested in? Do you know its approximate price? Do you know how much of a car payment you could afford each month? Based on the payment you can afford, is this car within your reach? In this project, students will use a formula to calculate the number of months it will take them to pay off a car loan based on the amount of the loan, the amount of the monthly car payment, and an interest rate which they will get from an internet resource.
Logs are useful in the real world, but not in an anything pertaining to my life.
The logarithms are used in electronics to find the ranges of values like "Frequencies in the range of 1 Hz to 1000 MHz. Voltages in the range of nanovolts to kilovolts. Currents in the range of microamperes to amperes. Power levels from microwatts to kilowatts. Resistances from ohms to megohms. Capacitances from a few picofarads to thousands of microfarads. Inductances from microhenries to henries. " (play hookey, 2009). By using loarithms, a large nember can be written in a simple form.
After I seached abouth the use of loarithms, I understand that it is very helpful for many scientists. Yet, I do not I would use it in my real life.
One place in the real world where logarithms are actually used are in dealing with the pH scale in chemistry.
"The pH scale is used in chemistry to determine the acidity or alkalinity of a solution. The pH scale is actually a logarithm in the form: log[10](concentration of hydrogen ions). Thus, pH 1 = log[10]10, and pH 2 = log[10]100."
(http://library.thinkquest.org/C0110248/algebra/isllog.htm)
Honestly, I have absolutely no idea what that means. The pH scale ranges from 1 to 14, 1 being the most acidic. The pH of a solution on this scale can be found by using the equation pH=-log[H+], with [H+] being the concentration of H+ ions, in mol/L. I still really have no idea what that means, or how this scale works, considering I know nothing about chemistry.
As i sifted through the search results, i found a website by thinkquest. They seem to be an organization that helps with math. They have an article explaing that logarithms are used in the pH scale. This scale is used mostly for chemistry to measure the acidity or akalinity of water. They may not seem very useful, but it is. Anyone who has a pool must do daily tests to see how much chlorine and alkaline are in the pool. This uses the pH scale and therefore is used by millions everyday without even realizing it.
http://library.thinkquest.org/C0110248/algebra/isllog.htm?tqskip1=1&tqtime=1130
Engineering, physics, and even astronomy use logarithms. In astronomy, in particular, they use the log tables as aid computation, and have used these tables even before the invention of computers and calculators. (KryssTal, A Look at Logarithms- http://www.krysstal.com/logarithms.html)
Even though the mathematicians who used these tables were from the 1600's, it serves the point that even then they knew how to simplify equations to solve them easier. Now that we have calculators the work load has been dulled down for us, but that still doesn't mean that its easy to understand or even do.
Another webites informed me that logarithms are used to figure out the stellar magnitude or brightness of the stars above us. (http://www.dp.eric-fox.com/10th%20Grade/Sun_Stuff.htm)Using logarithms allows us to better know the brightness of the stars and the distance they are away from earth.
Sure, astronomy is cool just to look at the stars, but sometimes leaving things simply, keep them beautiful.
Another way that logarithms are present in the real world are in the form of discrete cryptography. Cryptography has been used for over 2000 years from the time of Julius Caeser by hiding secret messages. It has also been used in times of Harry Truman started under the NSA to keep this secret communication secret in order to attack opposing countries.
lauren cole
I bleieve that logarithms are useful in the real world for a couple of reasons. I think its is good to use for earthquakes so people know how much danger around them. It is also helpful because they can compare the strength of earthquakes and possibly predict a pattern for upcoming earthquakes. Even though they seem complicated they seem to be very helpful. I am interested in learning about these.
Logarithms are involved in measuring the loudness of sound in decibels. Decibels or dB are a logarithmic unit. Decibels can be defined as B = 10 log (I/H). I equals the
sound intensity which is usually measured in watts, while H is a reference to intensity. I'm not quite sure what a reference to sound intensity would be. Some examples or decibel ratings which are logarithms are: 30 dB is a whisper, 50 dB is normal conversation, and 120 dB is a rock concert. A reason why the this logarithm is important is because it is the only thing proportional to both the loudness of a sound and its intensity.
http://www.newton.dep.anl.gov/askasci/eng99/eng99325.htm
It is very interesting to think that logarithms are used is our daily conversations. But I still find it confusing, and I don't think I would ever be able to figure out the loudness of a sound in decibels by using the given logarithm for it.
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