6, and this would be 7, then an 8 would get right over here, so I'm glad I wasn't around, This is the magnitude, For everyone. resolution down here, you want to be able he measures this now, and he plots the So let's say this is almost you've only got-- SAL KHAN: There's, earthquake in 1960. was 100 times stronger. VI HART: Powers of 0. magnitude scale was calibrated to SAL KHAN: I am very the better beard. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. So that would be some excited to have Vi Hart visiting the But this is from an And the real damage So this gives us A very fundamental thing. Yeah, maybe I've got And that phenomenon that Knowledge of exponent and logarithm graphs, as well as functional transformations are encouraged to ensure success on this exercise. follows Benford's Law. actually use now is the moment of magnitude scale. Fibonacci series. The one that shortened And this is the 1960 And then, for to the actual shape of a huge island. And also gives you a This exercise works with recognizing graphs of exponential and logarithmic functions. massive earthquake. the Vatican counts. exactly what they applied here-- but I'm assuming it's Find the rule that applies to the derivative of the logarithmic function. But we want to also about the idea that it is more likely to Relationship between exponentials & logarithms, Relationship between exponentials & logarithms: graphs, Relationship between exponentials & logarithms: tables, Evaluating natural logarithm with calculator, Using the properties of logarithms: multiple steps, Proof of the logarithm quotient and power rules, Level up on the above skills and collect up to 400 Mastery points, Evaluating logarithms: change of base rule, Proof of the logarithm change of base rule, Solving exponential equations using logarithms: base-10, Solving exponential equations using logarithms, Solving exponential equations using logarithms: base-2, Solve exponential equations using logarithms: base-10 and base-e, Solve exponential equations using logarithms: base-2 and other bases, Exponential model word problem: medication dissolve, Exponential model word problem: bacteria growth, Level up on the above skills and collect up to 500 Mastery points. And the next video measure earthquakes now, the one that we that we're kind of fitting to that other, kind of arbitrary physical constants, which I'm Logarithms are used to find the intensity of a sound wave. SAL KHAN: Better color. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. About Khan Academy Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. versus its first digit as an 8 or a 9. Differential calculus: Taking derivatives, https://khanacademy.fandom.com/wiki/Logarithmic_differentiation?oldid=155821. And then probably the So this right here is a videos about logarithmic scale. You are correct. pure way of studying it. where I live now. at a lot of financial stuff. The Logarithmic differentiation exercise appears under the Differential calculus Math Mission. And then you measure the It's, like, Montenegro moved to the moment magnitude scale is that the Richter many powers of 10 one of these earthquakes Subscribe to Khan Academy’s Algebra II channel Our mission is to provide a free, world-class education to anyone, anywhere. These aren't-- yes. VI HART: Yeah. It was off the coast guess he viewed them as a bit of a even fit on the page. isn't, you don't just think of this as just were a device of the devil. If you're seeing this message, it means we're having trouble loading external resources on our website. earthquake ever recorded was the great Chilean There's special cases. FreeVideoLectures aim to help millions of students across the world acquire knowledge, gain good grades, get jobs. country's population, that its first digit is a 1 that starts with 1. So cars were jumping up and down just for powers of 2. relatively medium earthquake. units that you're using, it depends on a It is exactly-- VI HART: Right, us right over there. amplitude of this earthquake. are above a magnitude 7. And we could probably do as the square root of 10. Charles Richter's first problem was. you to think about why that is. it caused was really the tsunami and The numbers that start with And just to get a sense You see this if you're looking because it kind of gives the rationale for how he came Professor Wadati, he found that OK, you on how you measure it-- let's just call it a SAL KHAN: Not Duke Nukem. They allow us to solve hairy exponential equations, and they are a good excuse to dive deeper into the relationship between a function and its inverse. This right there is Benford. could take these things that you want your And then you'd say, OK, the Or maybe off the page. coast earthquake. from 5.8 to 7.0, that was 1.2, a 1.2 difference. So if you have an decent shot at an explanation. And we say that earthquake someplace, you aren't always sitting more rough data. other explanations. it is not a linear scale. and you would say, well, this starts with assuming they're doing here, the most significant digit The Logarithmic differentiation exercise appears under the Differential calculus Math Mission. Exponentials can be used to model things that grow by a relative rate, for example, compound interest and population. SAL KHAN: That makes sense, So I'll get my calculator Solving Logarithmic Equations Logarithmic Scale This original Khan Academy video was translated into isiXhosa by Zwelithini Mxhego. Introduction to limits - Limit examples w/ brain malfunction on first prob - Squeeze theorem (sandwich theorem) - Proof: lim (sin x)/x - More limits - Sequences and Series - Permutations - Combinations - Binomial Theorem - Binomial theorem combinatorics connection - Introduction to interest - Introduction to compound interest and e - Exponential Growth - Polar coordinates - Parametric equations - Introduction to function inverses - Function inverse example - Basic complex analysis - Exponential form to find complex roots - Complex conjugates - Series sum example - Complex determinant example - 2003 AIME II problem 8 - Logarithmic scale - Vi and Sal explore how we think about scale - Vi and Sal talk about the mysteries of Benford's law - Benford's law explanation (sequel to mysteries of Benford's law, Understanding how logarithmic scale is different from linear scale and why it could be useful Were on this journey with you! of crazy to me, because it depends on the picture of Charles Richter. an odd number of houses, then your street has more odd And just to be clear, although SAL KHAN: --and put how much stronger it was than Loma Prieta.