Problem 1: prove change of base formula (by example)

Problem 2: explore the recent paper about the eml function defined as exp(x)-log(y)

Problem 3: standard log stuff e.g. what is 1/log_b(a)?

Problem 4:
If log_3(log_3^a(log_3^b(3^90))) = 0, then what are the possible values of a+b?

#iTeachMath ♾️

+1 same Tue solve #2solve

Pillsbury doughboy in stitches

not ideal for the directions. otoh, if you *did* see such a dial... you might be already too far gone. win win or lose lose, not sure

I wonder whether exp & log are the only pair of inverse functions that can generate a particular set of standard functions(?) Like, can this be transformed into a criterion that uniquely determines exp & log??? Maybe I'll post this on MathOverflow if the spirit strikes

do you see the dial that is set on insane? turn it to sane. 🎛️

pushing my buttons

I put "enter" into the doc, no credit there but credit here

Credit: Avery

yes lol

and #4 has some stuff I need to edit around numbering...

hopefully you've seen the full problem set, I posted it somewhere! like, on bsky

RE: values in Desmos
idk! could page Eli others and find out for sure... I haven't actually experimented w the intermediate complexity of this function

there are some lists on bsky, whoever i am following is visible... but also, twitter built up a lot over the years and nothing has really *replaced* it. yet!

How do I prove that $f(x)f(y)=f(x+y)$ implies that $f(x)=e^{cx}$, assuming f is continuous and not zero? This is part of a homework assignment for a real analysis course taught out of "Baby Rudin." Just looking for a push in the right direction, not a full-blown solution. We are to suppose that $f(x...

this is roughly the proof on my mind when assuming it's a continuous function of a real variable:
math.stackexchange.com/a/293384/37122

Is there a name for function with the exponential property $f(x+y)=f(x) \cdot f(y)$? I was wondering if there is a name for a function that satisfies the conditions $f:\mathbb{R} \to \mathbb{R}$ and $f(x+y)=f(x) \cdot f(y)$? Thanks and regards!

math.stackexchange.com/questions/22...

I find it psychologically easier to have a smaller or more friendly leading coefficient lol

Have you seen the method of factoring e.g. in this case

6z² - 23z + 20

in order to factor the original?

In other words, reversing the order of the coefficients to find the factorization

Problem 1: prove change of base formula (by example)

Problem 2: explore the recent paper about the eml function defined as exp(x)-log(y)

Problem 3: standard log stuff e.g. what is 1/log_b(a)?

Problem 4:
If log_3(log_3^a(log_3^b(3^90))) = 0, then what are the possible values of a+b?

#iTeachMath ♾️

Play With Your Math

ps. To clarify that is CiCi as in the cocreator of PlayWithYourMath dotcom!
playwithyourmath.com

cc. #iTeachMath ♾️

follow along! 🪄 ✨ 🔮

anyway: hopefully the problem set i wrote amuses somebody!

when is it the case that, for function inverses f and g, f(x)-g(y) can generate the K-12 functions?

that's what i think is cool:
exp(x)-log(y)
generates lots of familiar stuff!

i don't have the intuition that it would allow you to get e.g. sin and arcsin, or even the arithmetic operations...

Okay! It is now part of a problem set, cc: #iTeachTrig 📐

Full problem set:
docs.google.com/document/d/1...

See Problem 3 for the relevant material.
(PS: Check out Problem 4, possibly without the scaffolding, if you want a fun challenge!)

#iTeachMath ♾️ 🤝 🧮 #MathSky

Logical NOR - Wikipedia

i took a math logic course that proved everything using IF-THEN and NOT, since you can reduce other logical connectives using them, and the proofs of various properties aren't unwieldy in length.

i recall that the Logical NOR* could be used alone for this purpose!
en.wikipedia.org/wiki/Logical...

a figure from the paper that indicates how you can nest x, y, and 1 with the eml function to get a familiar binary operation

in writing a problem set for Precalculus students, I included the following question (see image below)

spoiler:
www.desmos.com/calculator/l...

note about spoiler:
there is too much nested to plug in large numbers

cc. #iTeachMath ♾️ #MathSky 🧮

Same Mon #2solve,
peak ice hockey in Philly

we did minimum problems for fun, but these are straightforward once you realize a general technique; specifically, if you know how to distribute n cookies among 3 people, then if you say "everyone gets at least one cookie" you can first give them each one, then solve for n-3 cookies among 3 people.

same Sun minimal #2solve!

Simon count: 2
Women count: 0

#MathSky 🧮 #iTeachMath ♾️

Breakthrough Prize – Mathematics Breakthrough Prize – Laureates

Congrats to 3,000,000 USD Mathematics Breakthrough Prize winner, Frank!
breakthroughprize.org/Laureates/3/...

He joins Dennis, Simon, Daniel, Takuro, Martin, Alex, Vincent, James & Christopher, Jean, Ian, Richard & Terence & Jacob & Maxim & Simon.

So far: 100% male laureates.

Spend the $ wisely!

the first newsletter i've... ever subscribed to???
on purpose, at least! #iTeachMath #MathSky

cool

You have crossed out some entries e.g. (5,5,0) more than once. So, count entries for which (in this problem) 5 appears more than once.

The result is a problem at the intersection of stars and bars & inclusion-exclusion.

A very good high school challenge!

🍪 #iTeachMath ♾️ #MathSky 🧮