Is 3⁴⁴ or 4³³ larger? #Shorts #algebra #math #education

[mumujibirb]

Bruh, usually if the exponent is larger, it almost always wins, unless the difference is small
Disclaimer:
Please use common sense before applying this trick. As stated above, IT DOES NOT ALWAYS WORK.

[saahilsaiyed]

This is how i would solve this: 4 to the power 33 looks like an answer they'd want me to choose. Sooo... Let's go with 3 to the power 44

[rudrarana]

Actually a more general proof is that for a^b vs b^a, if e<a<b a^b is bigger than b^a, bprp did a great video on it

[kepler]

U have to use x^x function as it increasing in >e and decreasing in 0<x<e 🤗

[generaldanghor]

First math channel that doesn’t show completely trivial things. Nice 👍

[МихаилКолосков]

Interesting fact:
If you have a^c and b^d, where a/d=b/c and e<a<b then a^c>b^d

[sharathbm]

Sir please Make this type of videos. Its really helps somebody

[kenannetekimpasaevren]

Did it with ln fonction at calculus. Dudes here is a tip for you:
R--->R f(x), g(x)
f(x)= a^x g(x)=x^a
If a>x and a>e (euler):
g(x)>f(x)
If a>x and a<e:
f(x)>g(x)

Example:
9^10>10^9
2^1>1^2
-3^-5>-5^-3
...

[livedandletdie]

Doesn't matter if a^n or b^m as long as n>m a^n is bigger. Unless you have a base b>>a..

[Assterix]

There are faster situational methods that are also simpler.

[Nedums]

bro just taught me something in under 60 seconds meanwhile a teacher has to take 20 minutes to explain it

[ramech]

Assuming 4^33 > 3^44, let check if that is correct.

We take the natural logarithm on both sides: ln(4^33) > ln(3^44)
<=> 33 ln(4) > 44 ln(3)
We divide by 44
<=> 3/4 ln(4) > ln(3)
<=> ln(4^(3/4)) > ln(3)
<=> 4^(3/4) > 3
<=> sqrt(8) > 3
<=> 8 > 9

Which is indeed false, so 3^44 must be over 4^33.

[anshumanrath]

Their logarithm should also be larger
3^44 into log - 44 log 3
4^33 into log - 66 log 2
We know log 2 = 0.693 and log 3 = 1.0986
44log3 = 48.33
66log 2 = 45.73

Hence 3^44 should be greater

[zeptopiagaming]

I think this is how to solve the problem. First take 3to the power of 44.44 consists of two digits so 11.so it becomes (3to the power of 4) 11.As it became 3 to the power of 4 multiply it four times 3×3×3×3 so it becomes 81powered by 11.same for the second one. Then he compared 81 and the other number and got the answer I think

[jasthakker]

This also is a great example of the power of compounding

[shizumeru_]

You could also do 44ln(3) > 33ln(4), knowing that the two ln's would close to 1 and only different by a small amount so ~44 > ~33.

[jeetard_]

Can also be solved by the graph of f(x)=x^(1/x)

[kanjanathevik]

I really really desperately need your videos like these, thank you very much 👍👍❤️

[bookpage]

Your teaching me more than my math teacher

[javier]

Calculator: *allow me to introduce myself*