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About this Lesson
 Type: Video Tutorial
 Length: 6:53
 Media: Video/mp4
 Use: Watch Online & Download
 Access Period: Unrestricted
 Download: MP4 (iPod compatible)
 Size: 73 MB
 Posted: 11/18/2008
This lesson is part of the following series:
College Algebra: Full Course (258 lessons, $198.00)
College Algebra Review (30 lessons, $59.40)
Algebra: Exponential and Logarithmic Functions (36 lessons, $49.50)
College Algebra: Evaluating Logarithms (4 lessons, $5.94)
This lesson will show you how to find the value of a logarithm. We will also practice with different bases, logs with radicals, logs in exponents and logs of mixed numbers and fractions. You will go over problems like log (base 6) of 36 = ? Or 6^[log (base 6) 28] = ?
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 http://www.thinkwell.com/student/product/collegealgebra. 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 UTAustin 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, padic 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
 Thinkwell
 2174 lessons
 Joined:
11/13/2008
Founded in 1997, Thinkwell has succeeded in creating "nextgeneration" 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 technologybased textbooks. For more information about Thinkwell, please visit www.thinkwell.com or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.
Thinkwell lessons feature a starstudded cast of outstanding university professors: Edward Burger (PreAlgebra through...
More..Recent Reviews
 log functions are awesome!
 01/19/2009

This is a very basic overview of finding simple log function values. Professor Burger's style is perfect since he gives specific problems and explains each step to solve that problem. He also gives great tips to help solve certain problems. Even the more difficult log problems are manageable if you watch this lesson.
All right, let’s now take a look at actually finding the values of logarithms. So again, just more practice with the logs. So let’s take a look at the following: log6 of 36, and I want to know what does that equal. Well, now I’m going to start to write a little bit less and think a little bit more. So a log is an exponent. So this mystery number is the exponent that I have to raise 6 to in order to make it equal 36. And so what is that? Well, 6 to what power equals 36? The answer is 2, so it equals 2.
Let’s try another one together. How about this one? log3 81. Why don’t you give this a shot right now and see if you can figure out what green number I should write in here, remembering that a log is the exponent. Give it a shot.
Okay, well 3 to what power gives me 81? I think it’s 34 because 3 times 3 is 9 times 3 is 27, times another 3 is 81. So log3 81 is 4. I hope you’re getting into the habit of seeing sort of like a backwards thing. I’m thinking of the exponent that I have to raise a number to in order to make it something else. We used to say, “What’s 34?” and you would say, “81.” Now I’m saying, “What power of 3 do I have to put in there to make it equal 81?” and you’ve got to say, “The fourth.” That’s what a log is.
All right, now they’re going to get harder. Sorry, sorry, sorry. How about this one? log4 . I don’t even know if I should make this interactive or not. In fact, I’ll just do this one for you because this is just way too tricky, I think. You’ve got to see this once and then you can do them all.
I look at this and after my initial panic mode, what I try to do is see if I can write this just in terms of 4’s, and I can if I’m careful, because I could write this in the following way. In fact, let me just focus for a second on just this term in here. So let me just focus on that for a second. . Let me cover this up so you don’t even think about the other thing. Just . I want to make everything work with 4’s in it, because I’m taking this thing with respect to a base of 4. Well, 2, I could write as 4 by doing the following. That’s just the . The is 2. But now I can write this as 41/3 divided by 41/2, changing all the roots to exponents, and then remember that the laws of exponents work in the following way. If I have the same bottom, but I’m taking quotients, then I subtract the exponents. So this actually equals 41/31/2, which equals 4 to… What power is that? Well, if you’re careful with combining the common terms and putting it over 6, you’ll see 2  3, which is a 1/6. So, in fact, after all is said and done, I see that this thing right here, which I remind you, appears right here, that equals 41/6. So this actually is just log4 41/6. Well, now this problem is actually a lot easier. In fact, I’ll make this problem now interactive. See if you can now figure out what number this should be. Try it now. Remember, I’m taking log4 41/6. Give it a shot.
Well, the question is this will equal the exponent that I have to raise 4 to in order to have it equal 41/6. Well, the answer must be 1/6 That’s the exponent I have to raise 4 to in order to make it equal that, because I have 41/6 and that would equal 41/6. So, in fact, when you see log base something of something to a power that will just equal the power. So loga a3 will equal 3. Logw w17 will equal 17.
Okay, one last one. How about 6 raised to the power log6 28? So what I’m asking for here is 6 raised to the power log6 28. This is a real tonguetwister kind of question, and let me try to do it for you. Let me just tell you one little thing. When I first started thinking about these things when I was younger, I could not understand the answer to this, and my teacher kept saying it to me again, and again, and again, and kept trying to explain it to me. Every time she explained it to me I still couldn’t understand it, and she was an amazing teacher. So don’t be frustrated. This takes a while. It took me forever. Then finally, one day you’ll see it, and you’ll go, “Oh, my God. Of course. Yeah.” But until then, it’s complete nothing.
Look, what is this? A log is an exponent. So this is the exponent that I have to raise 6 to in order to make it equal to 28. So this number right here is the exponent that if I raise 6 to it, I get 28. So what is 6 to that exponent? It’s 28. Because this is the exponent that I have to raise 6 to in order to make it equal 28. So if I take 6 and raise it to that exponent, I must get 28. Do you see it? I didn’t see it forever. Maybe you don’t see it. This is the exponent that I have to raise 6 to in order to get 28. That means if I take 6 to this power I must get 28. Well, look. Here’s 6 to that power. So it must equal 28. Maybe it seems weird to you, but if it does, stay the course and it’ll be clear. If you think about it though, that’s all I’m doing here. Log is the exponent I have to raise 6 to in order to make it equal 28.
All right, we’ll try some more log stuff up next.
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This is a very basic overview of finding simple log function values. Professor Burger's style is perfect since he gives specific problems and explains each step to solve that problem. He also gives great tips to help solve certain problems. Even the more difficult log problems are manageable if you watch this lesson.