#logarithms — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #logarithms, aggregated by home.social.
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Alright, future engineers!
A **Logarithm** answers What exponent do I need?. `log_b(x)=y` means `b^y=x`.
Ex: `log_2(8) = 3` because `2^3 = 8`.
Pro-Tip: `log(x)` (no base) usually means base 10; `ln(x)` means natural log (base e)!
#Algebra #Logarithms #STEM #StudyNotes -
Alright, future engineers!
A **Logarithm** is the exponent you raise a base to get a certain number.
Ex: `log_10(100) = 2` because `10^2 = 100`.
Pro-Tip: Logs simplify complex multiplications/divisions into easier additions/subtractions!
#Algebra #Logarithms #STEM #StudyNotes -
Alright, future engineers!
**Logarithms** are the *inverse* of exponentiation. `log_b(x) = y` means `b^y = x`. Ex: `log_10(100) = 2` (`10^2 = 100`). Pro-Tip: They turn multiplication into addition, simplifying complex calculations (e.g., pH, decibels)!
#AlgebraHacks #Logarithms #STEM #StudyNotes -
Alright, future engineers!
A **Logarithm** is the exponent 'y' a base 'b' needs to be raised to get 'x'. Ex: `log_b(x) = y` is equivalent to `b^y = x`. Pro-Tip: Use log properties to turn multiplication into addition, simplifying tough equations!
#Algebra #Logarithms #STEM #StudyNotes -
Alright, future engineers!
**Logarithms** tell you what power a base needs to be raised to for a given number. Ex: log_2(8) = 3 because 2^3 = 8. Pro-Tip: Logs simplify complex multiplication into addition! Master them for signal processing.
#Algebra #Logarithms #STEM #StudyNotes -
📸🤯 "This picture broke my brain!" said no one ever after watching a #3B1B video on #logarithms. Because, really, who doesn't crave a deep dive into the thrilling world of image transformations? 🤓🎉 Meanwhile, #Google LLC is busy ensuring that your brain remains blissfully unbroken by updating #YouTube terms and policies that you've definitely read. 📜👍
https://www.youtube.com/watch?v=ldxFjLJ3rVY #imageTransformations #updates #brainBuzz #HackerNews #ngated -
100 000 Years to Coinflip 5/10 Solve it with logarithms and you get the answer: about 138,629 years of buying 5 tickets per year. 📐 #Logarithms #FiftyPercent #TimeScale
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#OnThisDay #SpaceShuttle #Columbia disintegrated during reentry into the Earth's atmosphere (2003) resulting in the deaths of all seven crew members.
Birth Anniversary of Emilio Segrè (1905) - #NobelPrize winner and group leader for the #Manhattan Project. He discovered the elements #Technetium and #Astatine.
Birth Anniversary of John Napier (1550) - best known as the discoverer of #Logarithms.
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#OnThisDay #SpaceShuttle #Columbia disintegrated during reentry into the Earth's atmosphere (2003) resulting in the deaths of all seven crew members.
Birth Anniversary of Emilio Segrè (1905) - #NobelPrize winner and group leader for the #Manhattan Project. He discovered the elements #Technetium and #Astatine.
Birth Anniversary of John Napier (1550) - best known as the discoverer of #Logarithms.
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#OnThisDay #SpaceShuttle #Columbia disintegrated during reentry into the Earth's atmosphere (2003) resulting in the deaths of all seven crew members.
Birth Anniversary of Emilio Segrè (1905) - #NobelPrize winner and group leader for the #Manhattan Project. He discovered the elements #Technetium and #Astatine.
Birth Anniversary of John Napier (1550) - best known as the discoverer of #Logarithms.
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#OnThisDay #SpaceShuttle #Columbia disintegrated during reentry into the Earth's atmosphere (2003) resulting in the deaths of all seven crew members.
Birth Anniversary of Emilio Segrè (1905) - #NobelPrize winner and group leader for the #Manhattan Project. He discovered the elements #Technetium and #Astatine.
Birth Anniversary of John Napier (1550) - best known as the discoverer of #Logarithms.
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#OnThisDay #SpaceShuttle #Columbia disintegrated during reentry into the Earth's atmosphere (2003) resulting in the deaths of all seven crew members.
Birth Anniversary of Emilio Segrè (1905) - #NobelPrize winner and group leader for the #Manhattan Project. He discovered the elements #Technetium and #Astatine.
Birth Anniversary of John Napier (1550) - best known as the discoverer of #Logarithms.
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@startswithabang
I say, that's handy! -
Euler–Mascheroni constant! :euler:
In fact, the last one is:
\[\large\displaystyle\int_1^{+\infty}\mathrm dx\ \left(\frac{1}{\lfloor x\rfloor}-\frac1x\right)=\gamma\approx0.5772156649\]Equivalently,
\[\large\displaystyle\lim_{n\to\infty}\left(\sum_{k=1}^n \frac1{k}-\ln n\right)=\gamma=0.5772156649\ldots\]
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Unsolved problem in mathematics:
Is Euler–Mascheroni constant irrational? If so, is it transcendental?#Euler #Mascheroni #EulerMascheroni #Constant #gamma #EulerConstant #EulersConstant #EulerMascheroniConstant #Irrational #Irrationality #Transcendental #Transcendence #Unsolved #UnsolvedProblem #Maths #Mathematics #Indeterminate #IndeterminateForm #IndeterminateForms #Inf #Infinity #HarmonicNumber #HarmonicNumbers #HarmonicSeries #Logarithm #Log #Logarithms #NaturalLogarithm #Integral #ImproperIntegral
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An excellent general result.
If \(\Re(s)>1\),
\[\displaystyle\int_0^\infty\frac{\ln x}{x^s+1}~\mathrm dx=\frac{\pi^2}{4s^2}\left[\sec^2\left(\frac{\pi}{2s}\right)-\csc^2\left(\frac{\pi}{2s}\right)\right]\]Special cases:
\[\displaystyle\int_0^\infty\frac{\ln x}{x^2+1}~\mathrm dx=0\]
\[\displaystyle\int_0^\infty\frac{\ln x}{x^3+1}~\mathrm dx=-\frac{2\pi^2}{27}\]
\[\displaystyle\int_0^\infty\frac{\ln x}{x^4+1}~\mathrm dx=-\frac{\pi^2}{8\sqrt2}\]
\[\displaystyle\int_0^\infty\frac{\ln x}{x^5+1}~\mathrm dx=-\frac{4\pi^2}{25}\left(\frac{2+\sqrt5}{5+\sqrt5}\right)=-\frac{(5+3\sqrt5)\pi^2}{125}\]#Integral #Integrals #GeneralResult #GeneralResults #Result #Results #Logarithms #Logarithm #Integration #DefiniteIntegral #Calculus #IntegralCalculus
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#OnThisDay #SpaceShuttle #Columbia disintegrated during reentry into the Earth's atmosphere (2003) resulting in the deaths of all seven crew members.
Birth Anniversary of Emilio Segrè (1905) - #NobelPrize winner and group leader for the #Manhattan Project. He discovered the elements #Technetium and #Astatine.
Birth Anniversary of John Napier (1550) - best known as the discoverer of #Logarithms.
-
#OnThisDay #SpaceShuttle #Columbia disintegrated during reentry into the Earth's atmosphere (2003) resulting in the deaths of all seven crew members.
Birth Anniversary of Emilio Segrè (1905) - #NobelPrize winner and group leader for the #Manhattan Project. He discovered the elements #Technetium and #Astatine.
Birth Anniversary of John Napier (1550) - best known as the discoverer of #Logarithms.
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Here are a few #horsetail plants, seen on my walk #today (yesterday, actually).
Plus a wandering "woolly bear" (#TigerMoth) #caterpillar.
Horsetails are 150 million-year-old living fossils that were eaten by - yes! - Jurassic #dinosaurs.
Also, their unique node spacing inspired #JohnNapier in 1614 to invent #logarithms.
Admittedly, some rude US jurisdictions (wtf Oregon...?) classify them as noxious weeds.
But imho this is an amazing plant with a wonderful résumé 💚
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The #irony is palpable: a piece on #logarithms that's as accessible as a locked vault in Fort Knox, courtesy of #ModSecurity 😂🔒. This riveting read on mathematical history has been replaced by the stark beauty of a 406 error page—truly a triumph of modern web design! 🚫📉
https://www.lostartoflogarithms.com/ #webdesign #406error #mathhistory #HackerNews #ngated -
Euler–Mascheroni constant! :euler:
In fact, the last one is:
\[\large\displaystyle\int_1^{+\infty}\mathrm dx\ \left(\frac{1}{\lfloor x\rfloor}-\frac1x\right)=\gamma\approx0.5772156649\]Equivalently,
\[\large\displaystyle\lim_{n\to\infty}\left(\sum_{k=1}^n \frac1{k}-\ln n\right)=\gamma=0.5772156649\ldots\]
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Unsolved problem in mathematics:
Is Euler–Mascheroni constant irrational? If so, is it transcendental?#Euler #Mascheroni #EulerMascheroni #Constant #gamma #EulerConstant #EulersConstant #EulerMascheroniConstant #Irrational #Irrationality #Transcendental #Transcendence #Unsolved #UnsolvedProblem #Maths #Mathematics #Indeterminate #IndeterminateForm #IndeterminateForms #Inf #Infinity #HarmonicNumber #HarmonicNumbers #HarmonicSeries #Logarithm #Log #Logarithms #NaturalLogarithm #Integral #ImproperIntegral
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#Gravitational waves from giant #BlackHole collision reveal long-sought ‘ringing’ : Nature
Don’t Fall for Big Oil’s #CarbonCapture #Deceptions : Sci Am
The True Nature of #Logarithms : Medium
Check our latest #KnowledgeLinks
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Just like Magnitude. What could be simpler?
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The Lost Art of Logarithms
https://www.lostartoflogarithms.com/ – Fantástica iniciativa con una cantidad ingente de información sobre los logaritmos
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A work in progress, but I'm keeping an eye on this.
"An online book-in-progress by Charles Petzold wherein is explored the utility, history, and ubiquity of that marvelous invention, logarithms including what the hell they are; with some demonstrations of their primary historical application in plane and spherical trigonometry."
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“How Does A Computer/Calculator Compute Logarithms?”, Zach Artrand (https://zachartrand.github.io/SoME-3-Living/).
Via HN: https://news.ycombinator.com/item?id=40749670 (which provides important addenda)
#Calculator #Mathematics #Maths #Logarithms #TaylorSeries #NumericalMethods #NumericalAnalysis #FastMath
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Joost Bürgi and Logarithms - Logarithms are a common idea today, even though we don’t use them as often as we u... - https://hackaday.com/2024/02/27/joost-burgi-and-logarithms/ #retrocomputing #logarithms #sliderule
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The properties of use are:
1. Logarithm is monotonic
2. logₙ(𝑛) = 1
3. 𝑙𝑜𝑔ₙ(𝑎𝑏)=logₙ(𝑎)+logₙ(𝑏)
4. logₙ(√𝑛)=1/2log₃(2) is smallest since it is the only numbers <1.
log₅(10) is 1 + log₅(2) which is < 1.5 since the square root of 5 is more than 2.
log₄(8) = log₄(4) + log₄(2) = 1.5
log₂(3) = log₂(2) + log₂(3/2) = 1 + log₂(1.5) > 1 + log₂(√2) = 1.5
The key is to figure out where the numbers lie with respect to 1 and 1.5. That gives the ordering:
log₃(2) < log₅(10) < log₄(8) < log₂(3)
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Count Leading Zeros for Efficient Logarithms - [Ihsan Kehribar] points out a clever trick you can use to quickly and efficiently ... - https://hackaday.com/2023/02/07/count-leading-zeros-for-efficient-logarithms/ #softwaredevelopment #digitalaudiohacks #countleadingzeros #algorithms #logarithms #dsp
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Rubber Band “Slide Rule” Doesn’t Slide, but Rotates - Around here we mostly enjoy slide rules. We even have our own collections includin... - https://hackaday.com/2022/04/04/rubber-band-slide-rule-doesnt-slide-but-rotates/ #logarithms #mischacks #sliderule #math
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The #irony is palpable: a piece on #logarithms that's as accessible as a locked vault in Fort Knox, courtesy of #ModSecurity 😂🔒. This riveting read on mathematical history has been replaced by the stark beauty of a 406 error page—truly a triumph of modern web design! 🚫📉
https://www.lostartoflogarithms.com/ #webdesign #406error #mathhistory #HackerNews #ngated -
The #irony is palpable: a piece on #logarithms that's as accessible as a locked vault in Fort Knox, courtesy of #ModSecurity 😂🔒. This riveting read on mathematical history has been replaced by the stark beauty of a 406 error page—truly a triumph of modern web design! 🚫📉
https://www.lostartoflogarithms.com/ #webdesign #406error #mathhistory #HackerNews #ngated -
The #irony is palpable: a piece on #logarithms that's as accessible as a locked vault in Fort Knox, courtesy of #ModSecurity 😂🔒. This riveting read on mathematical history has been replaced by the stark beauty of a 406 error page—truly a triumph of modern web design! 🚫📉
https://www.lostartoflogarithms.com/ #webdesign #406error #mathhistory #HackerNews #ngated -
“How Does A Computer/Calculator Compute Logarithms?”, Zach Artrand (https://zachartrand.github.io/SoME-3-Living/).
Via HN: https://news.ycombinator.com/item?id=40749670 (which provides important addenda)
#Calculator #Mathematics #Maths #Logarithms #TaylorSeries #NumericalMethods #NumericalAnalysis #FastMath
-
“How Does A Computer/Calculator Compute Logarithms?”, Zach Artrand (https://zachartrand.github.io/SoME-3-Living/).
Via HN: https://news.ycombinator.com/item?id=40749670 (which provides important addenda)
#Calculator #Mathematics #Maths #Logarithms #TaylorSeries #NumericalMethods #NumericalAnalysis #FastMath
-
“How Does A Computer/Calculator Compute Logarithms?”, Zach Artrand (https://zachartrand.github.io/SoME-3-Living/).
Via HN: https://news.ycombinator.com/item?id=40749670 (which provides important addenda)
#Calculator #Mathematics #Maths #Logarithms #TaylorSeries #NumericalMethods #NumericalAnalysis #FastMath
-
“How Does A Computer/Calculator Compute Logarithms?”, Zach Artrand (https://zachartrand.github.io/SoME-3-Living/).
Via HN: https://news.ycombinator.com/item?id=40749670 (which provides important addenda)
#Calculator #Mathematics #Maths #Logarithms #TaylorSeries #NumericalMethods #NumericalAnalysis #FastMath
-
Here are a few #horsetail plants, seen on my walk #today (yesterday, actually).
Plus a wandering "woolly bear" (#TigerMoth) #caterpillar.
Horsetails are 150 million-year-old living fossils that were eaten by - yes! - Jurassic #dinosaurs.
Also, their unique node spacing inspired #JohnNapier in 1614 to invent #logarithms.
Admittedly, some rude US jurisdictions (wtf Oregon...?) classify them as noxious weeds.
But imho this is an amazing plant with a wonderful résumé 💚
