Nancy is on a new channel, NancyPi! New videos with Nancy will be at: https://youtube.com/NancyPi Follow: http://instagram.com/mathbff http://facebook.com/mathbff http://twitter.com/mathbff What are logarithms and how do you evaluate them? To skip ahead: 1) For how to understand and evaluate BASIC LOGS, skip to time 0:52. 2) For how to evaluate weirder logs, including the log of 0, 1, a FRACTION, or a NEGATIVE number, skip to time 6:44. 3) For NATURAL LOGS (LN X), skip to time 11:17. 4) For even weirder logs, including SOLVING for X and using the CHANGE-OF-BASE formula, skip to time 14:56. 1) BASIC LOGS: you can read log notation as "log, base 3, of 9 equals X". The small (subscript) number is called the base. You can always evaluate a log expression by rearranging it into something called exponential form. Every log expression is connected to an exponential expression. In this example, the log is connected to the exponential form "3 to the X power equals 9". This means, "3 raised to what power gives you 9?" Since 3 raised to the power of 2 equals 9, the answer for X is 2. This is also the answer for the value of the log expression. The log is always equal to the power (or exponent) in the exponential version, and in this case it equals 2. If you want, you can find the log value in your head just by asking yourself what power you need in order to turn the base number into the middle number ("argument" number). Note: if there is no base number in the log expression (no little subscript number), then the base is 10, since 10 is the default base. 2) WEIRDER LOGS (log of 0, 1, a negative number, or a fraction): you can use the same steps to rearrange log expressions that have a fraction, negative number, 0, or 1 in them. You can still rearrange them to be in exponential form just like you can with the basic logs from earlier. The log of 1 will always be 0, since 0 is the only power that can turn a base into 1. The log of 0 will always be undefined, since no power can turn a base into 0. The log of a negative number is undefined in the real number system, since no real power can turn a positive base into a negative number. 3) NATURAL LOGS (ln x): the natural log is just a special type of log where the base is e (the special math constant e, which is approximately 2.718 if you plug it into your calculator). You can use the same steps for rearranging the log expression into exponential form. Just remember that ln x means log, base e. 4) EVEN WEIRDER LOGS (solving for X, change-of-base formula): even if there is an X variable in the log part of an equation, you can still rearrange the equation into exponential form. This will let you solve for X. Sometimes you might need to use the change-of-base formula to evaluate a log expression. If there is no whole number power you know that works, it may actually be a decimal power that you can find by using the change-of-base formula. For example, you can re-write log, base 2, of 7 as (log 7)/(log 2) and use your calculator to find the decimal number if you need it.
I created this video with the YouTube Slideshow Creator (http://www.youtube.com/upload) class student lecture hi
Understanding how logarithmic scale is different from linear scale and why it could be useful Watch the next lesson: https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_properties/v/richter-scale?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII Missed the previous lesson? https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_properties/v/solving-logarithmic-equations_dup_1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you! 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. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan Academy’s Algebra II channel: https://www.youtube.com/channel/UCsCA3_VozRtgUT7wWC1uZDg?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
This video gives the intuition behind logarithm (log). Logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.In mathematics, the logarithm is the inverse operation to exponentiation, just as division is the inverse of multiplication. That means the logarithm of a number is the exponent to which another fixed number, the base, must be raised to produce that number. For more on logarithms : https://en.wikipedia.org/wiki/Logarithm
Free trial at The Great Courses Plus: http://ow.ly/tKWt306Gg7a Dr James Grime discusses "e" - the famed Euler's Number. More links & stuff in full description below ↓↓↓ A bit extra from this video: https://youtu.be/uawO3-tjP1c More James Grime videos from Numberphile: http://bit.ly/grimevideos Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: https://teespring.com/stores/numberphile Other merchandise: https://store.dftba.com/collections/numberphile
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Watch my FIELD DAY video, “Home Sweet Whittier”: http://bit.ly/1QKKcuo And subscribe to FIELD DAY!! http://www.youtube.com/fieldday Jake and Kevin will be doing field days soon!! LINKS, SOURCES, and MORE are below: This video was shot in beautiful Bucharest, Romania :) my twitter: http://www.twitter.com/tweetsauce my instagram: http://www.instagram.com/electricpants music by http://www.youtube.com/JakeChudnow and http://www.audionetwork.com “How Old Can We Get?” Vsauce1 video: https://www.youtube.com/watch?v=6LyCC6jjcx8 The Universal History of Numbers: http://www.amazon.com/The-Universal-History-Numbers-Prehistory/dp/0471375683 Highest number counted to with one breath: https://recordsetter.com/world-record/highest-number-counted-breath/17691 Highest number counted to: https://recordsetter.com/world-record/highest-number-counted-to/13623 Video of Harper reaching one million: https://www.youtube.com/watch?v=_aqCC2PVNcA Jon Counts to 100,000 (part 1): https://www.youtube.com/watch?v=KMDjQHzRj6U Jon Eats Carrots: https://www.youtube.com/channel/UCVgEzGuc7zYLI0fi4rSNnGQ Jon Drinks Water: https://www.youtube.com/channel/UC15CpXEtQ4DH6UCE7kNcQOA PetitTube: http://www.petittube.com/ Vi Hart on logarithms and counting: https://www.youtube.com/watch?v=N-7tcTIrers Logarithmic perception: http://en.wikipedia.org/wiki/Weber%E2%80%93Fechner_law http://en.wikipedia.org/wiki/Stevens%27_power_law Thinking logarithmically: http://www.radiolab.org/story/91698-innate-numbers/ https://www.khanacademy.org/math/algebra2/exponential_and_logarithmic_func/log_functions/v/vi-and-sal-explore-how-we-think-about-scale http://www.science20.com/news_articles/logarithm_versus_linear_thinking_why_our_brains_midpoint_1_and_9_might_be_3-94891 http://www.huffingtonpost.com/ben-thomas/whats-halfway-between-1-and-9-kids-and-scientists-say-3_b_1982920.html psychophysics of price: http://www.researchgate.net/publication/24098883_Market_Price_Variation_Perceived_Price_Variation_and_Consumers'_Price_Search_Decisions_for_Durable_Goods subitizing: http://en.wikipedia.org/wiki/Subitizing approximate number system: http://en.wikipedia.org/wiki/Approximate_number_system numerical cognition: http://en.wikipedia.org/wiki/Numerical_cognition Panamath ANS test: http://www.panamath.org/testyourself.php Planck Length: http://www.physlink.com/Education/AskExperts/ae281.cfm interactive “scale of the universe”: http://htwins.net/scale2/
In math, exponents, logarithms, and roots all circle around the same idea, but the notation for each varies radically. The triangle of power is an alternate notation, which I find to be absolutely beautiful. (This is the corrected version of the one I put out a month or so ago, in which my animation for all the inverse operations was incorrect) Here's a sketch from the math redditer Cosmologicon showing how this might be usual with practical space considerations: http://i.imgur.com/hAeJokq.jpg This original comes from an answer to a math exchange post by Alex Jordan, which you can find here: http://math.stackexchange.com/questions/30046/alternative-notation-for-exponents-logs-and-roots I also briefly flashed a blog post with another interesting alternative for logarithm notation: http://www.solidangl.es/2015/04/a-radical-new-look-for-logarithms.html
In this follow-up video to his "e to the i pi for dummies" video the Mathologer sets out to properly explain the coolest features of the famous number e and the exponential function e^x. Find out WHY e is irrational, how you go about calculating the first 1,000,000 digits of e, WHY the exponential function e^x is its own derivative, etc. Here are links to the videos that I refer to in this video: e to the pi i for dummies: https://youtu.be/-dhHrg-KbJ0 (this is the video I summarise at the beginning) Indeterminate: the hidden power of 0 divided by 0: https://youtu.be/oc0M1o8tuPo (about derivatives, among other things) Math in the Simpsons: e to the i pi: https://youtu.be/Yi3bT-82O5s (this is the video that I refer to at the very end) This week's t-shirt I made myself. Check out this wiki page about this pretty identity https://en.wikipedia.org/wiki/Proof_that_22/7_exceeds_π Thank you very much to my friend Marty Ross for proofwatching drafts of this video and helping me to get the words "just right" and to Danil Dmitriev the official Mathologer translator for Russian for his subtitles. Enjoy! Burkard
What is 6÷2(1+2) = ? This problem went viral and generated millions of comments on Facebook, Twitter, YouTube and social media sites. I explain how to get the correct answer by using the modern interpretation of the order of operations. I also explain how you would get a different answer under historical usage of the division symbol. *I get many, many emails about this problem. Before you send an email, check out my blog post or in the links provided below which address every concern I have received so far. If you write to me about this be advised I probably will not respond. Blog (text explanation): http://wp.me/p6aMk-4OV Slate explains the history of the division symbol http://www.slate.com/articles/health_and_science/science/2013/03/facebook_math_problem_why_pemdas_doesn_t_always_give_a_clear_answer.html Here is a 1917 article from "The American Mathematical Monthly" that explains the usage of the division symbol as an exception to the order of operations http://www.jstor.org/stable/2972726?seq=1#page_scan_tab_contents Google evaluation https://www.google.com/#q=6%C3%B72(1%2B2) WolframAlpha evaluation http://www.wolframalpha.com/input/?i=6%C3%B72(1%2B2) If you like my videos, you can support me at Patreon: https://www.patreon.com/mindyourdecisions Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you. My Blog: https://mindyourdecisions.com/blog/ Twitter: https://twitter.com/preshtalwalkar Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965 Google+: https://plus.google.com/108336608566588374147/posts Pinterest: https://www.pinterest.com/preshtalwalkar/ Tumblr: https://preshtalwalkar.tumblr.com/ Instagram: https://instagram.com/preshtalwalkar/ Patreon: https://www.patreon.com/mindyourdecisions Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r If you buy from the links below I may receive a commission for sales. This has no effect on the price for you. My Books "The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.8/5 stars on 31 reviews) http://amzn.to/1uQvA20 "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 2 reviews) http://amzn.to/1o3FaAg "Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews. http://amzn.to/1GhUUSH "Math Puzzles Volume 2" is a sequel book with more great problems. (rated 5/5 stars on 3 reviews) http://amzn.to/1NKbyCs "Math Puzzles Volume 3" is the third in the series. (rated 3.8/5 stars on 4 reviews) http://amzn.to/1NKbGlp "40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.3/5 stars on 12 reviews) http://amzn.to/1LOCI4U "The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 4 reviews) http://amzn.to/18maAdo "Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 3 reviews) http://amzn.to/XRm7M4