#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!
**Logarithm:** Finds the exponent you need to raise a base to get a number.
Ex: `log_b(x) = y` means `b^y = x`.
Pro-Tip: Use change of base: `log_b(x) = ln(x)/ln(b)` for calculations!
#Algebra #Logarithms #STEM #StudyNotes -
Alright, future engineers!
**Logarithm:** The exponent 'y' a base 'b' needs to get 'x'.
Ex: `log_b(x)=y` is `b^y=x`. Think `log_2(8)=3` because `2^3=8`.
Pro-Tip: Logs turn mult/div into add/sub, simplifying complex calculations!
#Algebra #Logarithms #STEM #StudyNotes -
Alright, future engineers!
**Logarithm:** The exponent a base needs to be raised to for a given number.
Ex: `log_2(8) = 3` means `2^3 = 8`.
Pro-Tip: Logs 'undo' exponentiation! Essential for solving for variables in exponents.
#Algebra #Logarithms #STEM #StudyNotes -
Alright, future engineers!
**Logarithm:** The exponent you raise a base to get a number.
Ex: `log_2(8) = 3` because `2^3 = 8`.
Pro-Tip: Logs are inverse of exponents! Key for solving equations where the unknown is an exponent. -
🔢🤓 Breaking news: everything you ever learned about math is wrong, #logarithms are the universal truth! 💡 But wait—JavaScript isn't working, so good luck rendering those groundbreaking equations. Let's all just agree this blog post is the mathematical equivalent of reinventing the wheel, only to realize it's still round. 🌀
https://alexkritchevsky.com/2026/05/25/everything-is-logarithms.html #mathnews #JavaScript #issues #reinventingthewheel #groundbreakingequations #HackerNews #ngated -
Alright, future engineers!
**Logarithm (log_b x):** The exponent 'y' you raise base 'b' to, to get 'x'.
Ex: `log_2 8 = 3` because `2^3 = 8`.
Pro-Tip: They're inverses of exponentials! Essential for solving for unknown exponents (e.g., in decay models).
#Algebra #Logarithms #STEM #StudyNotes -
“In 1980, #Intel released the #Intel8087 #FloatingPoint coprocessor, a chip that could make math up to 100 times faster. As well as arithmetic and square roots, the 8087 computed #transcendental functions including #tangent, #exponentiation, and #logarithms.
But it all depended on a 69-bit adder: "The arithmetic heart of the floating-point execution unit is centered about a #nanomachine comprised of the adder and its related #registers, #shifters and control circuitry," as the patent describes it”
#Silicon / #EE / #Computing <https://www.righto.com/2026/06/intel-8087-adder-reverse-engineered.html>
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Alright, future engineers!
**Logarithm:** The exponent you need to raise a base to get a number.
Ex: log₂(8) = 3 because 2³ = 8.
Pro-Tip: Logs are inverses of exponentials! Use them to solve for exponents or scale vast data ranges.
#Algebra #Logarithms #STEM #StudyNotes -
Alright, future engineers!
**Logarithms** are the inverse of exponentiation: `log_b(x) = y` means `b^y = x`.
Ex: `log_2(8) = 3` because `2^3 = 8`.
Pro-Tip: Think 'what power of b gives me x?' Makes evaluating easy!
#Algebra #Logarithms #STEM #StudyNotes -
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 -
#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! -
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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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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#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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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
