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College Algebra: Distance Modulus Formula


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About this Lesson

  • Type: Video Tutorial
  • Length: 5:05
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 55 MB
  • Posted: 06/26/2009

This lesson is part of the following series:

College Algebra: Full Course (258 lessons, $198.00)
Algebra: Exponential and Logarithmic Functions (36 lessons, $49.50)
College Algebra: Applying Logarithmic Functions (2 lessons, $1.98)

Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers equations and inequalities, relations and functions, polynomial and rational functions, exponential and logarithmic functions, systems of equations, conic sections and a variety of other AP algebra, advanced algebra and Algebra II topics.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

About this Author

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Founded in 1997, Thinkwell has succeeded in creating "next-generation" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technology-based textbooks. For more information about Thinkwell, please visit or visit Thinkwell's Video Lesson Store at

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Well, welcome to outer space, the great frontier. Anyway, you know, space travel is great, and trying to understand the planets and where they're located and so forth actually is fantastic math and fantastic astronomy and it all comes together with a logarithm. So let's take a look at a logarithm question where we have that.
So here, you notice, is the sun. And it is hot, hot, hot. You don't want to touch that. Here's the earth. And first it goes behind me, and then it goes around the sun, and it goes back behind me. Anyway, if you want to actually compute the distance between let's say, here's a star that's far, far away, and if you want to compute the distance, it turns out that there's a really neat way of doing that that just involves logarithms. So I want to tell you about that right now. So let's watch the sun set.
And as the sun goes down on mathematics... The log appears. Apparently there was a log there. I wasn't expecting that. So if you want to find the distance, actually, between earth and a star, here's the formula. It's actually this m = 5log r and then -5. What's r? r is the distance actually in par seconds, and what is m? Well, m is the thing we're trying to find. M is actually the distance that a lot of times scientists use. This is called the "distance modulus," which is actually just the logarithm, in some sense, of the distance between two galactic things.
So, for example, suppose that the distance between earth and this particular star was actually 1.5. So that is the--the approximate distance of m for a star is 1.5, and what I want to do is I want to determine its distance from the earth. So I'm given m and I want to find r. So let's think about how we do that. So we're told that m = 1.5 and now my mission is to find r. So what do I do? Well, I know that 1.5 = 5log r - 5. So if I bring this -5 to this side, it becomes a +5 and so I see 6.5 = 5log r. If I divide both sides by 5, I would see that 6.5 divided by 5 equals log r. Now how can solve this? Well, remember a naked log is log[10] so actually you could convert this into the following: log is the exponent. 10 to that exponent will equal r, so what I have here is r = 10 to that exponent, 6.5 divided by 5. And so, in fact, what is that? Well, we can turn that on and we can see 6.5 divided by 5 equals 1.3, so 10^1.3, and so what does that equal? So you can work this out with a calculator. So 10^1.3 equals 19.95-stuff, and these units, by the way, the units here are now in par secs. So it's 19.95 par secs, and it turns out that one par sec is approximately 3.3 light years. So, in fact, 19.95 par secs, or actually that times 3.3 light years. If you want to know light years just multiply that by 3.3. So the star that I have in mind is 65.84 light years away from earth. Really, really far, and it turns out that this logarithmic measure turns out to be quite handy. So if you're given a logarithmic measure, you can easily figure out the actual measure just by plugging in and doing a little bit of log manipulation.
So log manipulations actually allow you to understand the planets. Have fun.
Exponential and Logarithmic Functions
Applying Logarithmic Functions
The Distance Modulus Formula Page [1 of 1]

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