Glad that I have come across your channel. Really learning a lot about maths, and despite not being the best at it, I do understand some of what is being taught, but slowly I’m learning 😊
This same guy has a fantastic youtube video for how to factor trinomials with integer coefficients over the integers where the leading coefficient is not equal to 1....It's a very clever method that I had never seen before even though I have been teaching math for over 20 years.
3 to the power 90 is larger Because you can use the exponent rule a^m x n= a^mn. So we must take the HCF of 120 and 30, so we get 30. We try to simplify more, so getting 2^4 x 30 and 3^3 x 30= 16^30 and 27^30. The exponent here is same, so we just need to compare the numbers. 16 is smaller, so 27^30 or 3^90 is larger
Thank you Sir for your videos! Kids today are fortunate to have lots of available resources to get additional info to learn. (If we had your channel before, perhaps I would've had a better grade in math.) 😊
I ❤ these videos! I discovered your content through suggested shorts and I am seeing some math concepts I either have not seen in years or never have seen before. But I always end up understanding & learning by the end. Thank you!
Use a calculator. If it were 2^47 and 3^29 you could round them to 2^40 and 3^30, perform the trick in the short, and then conclude that 2^47>3^29. It might be possible to prove that rounding 2^47 to 2^40 decreases that value by more than the amount that rounding 3^31 down to 3^30 does.
@@dhruvgarg1624 yes. I guess my point is that when there are no common factors in the exponents, it’s not as easy to make the exponents the same across the system. Now presumably you could look for a least common multiple of the pair, so you could make it (2^(1/31))^1457 and (3^(1/47))^1457 But again it’s not as easy to see which is larger (2^1/31) or 3^(1/47) the only thing that we can safely say is that they both should be fairly close to 1. However if we get a calculator out we can see that 2^(1/31) is 1.022 and 3^(1/47) is 1.023 so 3^31 should be larger than 2^47. I mean the trick still works it’s just that the base gets smaller instead of bigger. Since we are taking the original to the power of a whole number the bases gets larger while holding then exponents constant. The other where there are no common factors will get smaller because it will be taken to the power of a fraction while making the exponent common between the two. But the closer the two values are to each other the harder it is to approximate and see which is larger. When the percentage of difference is large it is relatively easy to see which is larger. But yes your chosen solution works just as nicely. I just find it harder to do roots and logarithms via mental math. This method is thus more effective when the exponents share a common factor.
I probably would have compared 120*log(2) with 90*log(3) to find out which one was bigger without a second thought, but his approach requires less knowledge of maths.
Theres a simple approximation i use for exponents. a to the b power = 10 to the (bloga) power. Using that, you can set both exponents at base 10, making them easier to compare. Common formula we use for science olympiad.
This problem not important to solve it because my teacher says which one bigger power on number its always small like 2120 or 390 than bigger power of 2120 so its is small 😅 that's it
Yeah it’s a fooIish comment. I think it only has likes as it introduces another way of thinking, cuz there’s no intelligence in it. Bro’s equality says 3≈1.5 as well 💀
No its not easy step we can multiple 2and 120 we get 240 and we can multiple 3 and 90 we get 270 hence we find the answer that which is greater it is easier than your step sir😅😅
This would complicate a bit if both exponents were prime numbers. Probably in that case taking logarythm of both expressions would be the fastest way to compare, but still might need a calculator.
I would have scored a centum in maths, if he was my teacher in school. Basics are very important and it's in the hands of the teacher to make the subject interesting. I am aged 49 and love all his videos.
Without watching the video: a^b = x can be rewritten to ln x = b*ln a. Since log is monotonic this operation keeps the relation. At least no arithmetic overflow anymore. Question now is if 120/90 = 4/3 > ln 3 / ln 2 or same way back 2^4 = 16 > 3^3 = 27. Well, same as in the video - factoring out gcd of exponent.
Both have number and power(we need to find which is bigger) 'in short cut multiple numbers with power-( 2×120=240) and (3×90=270)' hence 3⁹⁰ is great.it is very easy known?????
In my country, we memorize log_10(2) and log_10(3). 0.301… and 0.4771 respectively. 2^120 > 120*0.3 = 36 3^90 < 90*0.5 = 45 One is much larger. And we’re dealing with logs! So I think it’s safe to assume 3^90 >
Thank you so much.Excellent teaching,I liked that you used chalk.That’s what my teachers used in those days.Iloved the sound when the chalked talked with the blackboard.Nut there was some noise in the background like carpentry work.However your video is good and I am subscribed.Youtoube recommended it to me .Thanks a zillion.
I have a better technique but I don’t know if it counts : 2^120, u multiplied 2 by 6 and divide the exposant by 6 = 12^20 3^90 same but by 4 = 12^22,5 So 3^90 is higher
3^90= 8727963568087712425891397479476727340041449 (tredecillion) 2^120= one undecillion, three hundred and twenty-nine decillion, two hundred and twenty-eight nonillionth Therefore, 2^120
Sorry but the conclusion „and because base 16 is less than 30“ to „so 16^30 is less than 27^30“ is just mathematically nonsense. (-27)^30 is greater than (-16)^30 and -30
![KAYTRANADA - Witchy (feat. Childish Gambino) [Official Video]](http://i.ytimg.com/vi/jGK3YVmGZ3Y/mqdefault.jpg)
Good old white chalk! Even the sound of it slapping against the board brings back memories.
Btw isn't the shape of chalk a bit different. Guess nowadays physics is applied in factories in a better way to reduce friction
@@Veer.Thakkarhow did you somehow bring up science to such a simple comment, stfu
@@Veer.ThakkarI assume it's a chalk holder
@@maxpie16now that you mention it, I too think that now 😅
I’ll come
That chalk sound is brutal.
I think its satisfying.....😌😌
@@a.c.e__t.a.n.y.a_ same❤😅
I too👍🙂@@a.c.e__t.a.n.y.a_
Yes it is satisfying😊
Edit: Thanks for 10 likes please try to do more likes🥰
Yup it sure is...
Satisfying ❤
Other : understanding the question...
Me : seeing his triceps☠️
❤😂
Perve!🚩
Never skip exponent day 💪
the teacher:which is bigger, 2^120 or 3^90?
:your triceps
Same 😊
Which one is bigger
Me:YOUR TRICEPS!
💀💀
Youp broh
😢
Hu
Aaaaaw shiiiet, I thought I was going to be the only one commenting on that. Yeah, they're great! But he's only got it in his right arm.... hmmmmm
Bro got insane triceps just by writing on a board🗿
☠️don't underestimate math teacher they have super powers
Real
Realest comment section ever
He is not "bro "...he is a teacher 😢😢
Triceps
Glad that I have come across your channel. Really learning a lot about maths, and despite not being the best at it, I do understand some of what is being taught, but slowly I’m learning 😊
Full time gymer
Part time teacher😅
What the heck is gymer? 🤨
@@IamYou.-_- 😆I mean.. ...u understand that I know! Btw nice name I am You
i dont understand ✋
@@TechsumitX I didn't get it first......but, she's probably talking saying "Gym Rats" as "Gymer"
@Jack-pq4tt hehe
Mr.H's way of explaining is very simple which makes even a very difficult question easy.
That's true..
Dude this is taught in High school
Sorry if I step in but… this isn’t a very difficult question 😅 At least in Europe
I not like maths but l am profesar of maths😅😅
the chalk sound is so satisfying. 👌🏻
Thats literally one of the reasons I watch him.
But also to help me with math of course.
It sound I like he is beating I his child with belt
Non-blind people:- ok...okkk...ok i'm understanding the solution 😊
Blind people:- 🍌🥥☠️👽
i see this question on many electrician exams, you just made me an extra point or 2
👍
The best math profile. The prof is concise and to the point . No long tiring videos which are always confusing
This same guy has a fantastic youtube video for how to factor trinomials with integer coefficients over the integers where the leading coefficient is not equal to 1....It's a very clever method that I had never seen before even though I have been teaching math for over 20 years.
3 to the power 90 is larger
Because you can use the exponent rule a^m x n= a^mn. So we must take the HCF of 120 and 30, so we get 30. We try to simplify more, so getting 2^4 x 30 and 3^3 x 30= 16^30 and 27^30. The exponent here is same, so we just need to compare the numbers. 16 is smaller, so 27^30 or 3^90 is larger
Also sound of board is wow....
NOTE: I did not go through the video.. I applied some rules of exponents
Thank you Sir for your videos! Kids today are fortunate to have lots of available resources to get additional info to learn. (If we had your channel before, perhaps I would've had a better grade in math.) 😊
Sir...class okke set aan...🔥👍🏼
ella essay questionum eythan pattunna format venam 🛑🛑🛑
Hey mallu.....😂
Even the board is scared of this man
Great job sir! Thanks for the explanation.
I ❤ these videos! I discovered your content through suggested shorts and I am seeing some math concepts I either have not seen in years or never have seen before. But I always end up understanding & learning by the end. Thank you!
Any one watching in 5/3/2024😂👉
I'm in the US and it's still 1 May 24 (in my timezone). But I take it you're asking about 5 March 24. Maybe?
I like this trick of factorizing the exponent but what if we started with 2^47 and 3^31 where the exponents do not share any common factors?
Use a calculator. If it were 2^47 and 3^29 you could round them to 2^40 and 3^30, perform the trick in the short, and then conclude that 2^47>3^29.
It might be possible to prove that rounding 2^47 to 2^40 decreases that value by more than the amount that rounding 3^31 down to 3^30 does.
If you have a calculator... multiply the exponent by the log of the base, and compare.
2^47 =y
Log on both sides
47ln2 =lny
47×0.6 =lny=28.2
3^31=x
31ln3 =lnx=31 almost
Hence 3^31 is bigger
@@dhruvgarg1624 yes. I guess my point is that when there are no common factors in the exponents, it’s not as easy to make the exponents the same across the system.
Now presumably you could look for a least common multiple of the pair, so you could make it
(2^(1/31))^1457 and
(3^(1/47))^1457
But again it’s not as easy to see which is larger (2^1/31) or 3^(1/47) the only thing that we can safely say is that they both should be fairly close to 1.
However if we get a calculator out we can see that 2^(1/31) is 1.022 and 3^(1/47) is 1.023 so 3^31 should be larger than 2^47. I mean the trick still works it’s just that the base gets smaller instead of bigger. Since we are taking the original to the power of a whole number the bases gets larger while holding then exponents constant. The other where there are no common factors will get smaller because it will be taken to the power of a fraction while making the exponent common between the two.
But the closer the two values are to each other the harder it is to approximate and see which is larger. When the percentage of difference is large it is relatively easy to see which is larger.
But yes your chosen solution works just as nicely. I just find it harder to do roots and logarithms via mental math. This method is thus more effective when the exponents share a common factor.
Really admire MrH. He kniws his stuff, is clear and logical, doesnt use an AI or music and delivers clear answers. Thank you!
Great Teacher! Thank you só much.
Levi Malho (Portugal)
I probably would have compared 120*log(2) with 90*log(3) to find out which one was bigger without a second thought, but his approach requires less knowledge of maths.
Thank you, Professor!
i actually tend to hate asmr but that chalk is just amazing, please make a full video of just filling up a board with gibberish
It would be easier by taking log
120log2 and 90log3
120×0.3 and 90×0.5
36
The first time I have ever seen the greater exponent losing...
THAT'S WHAT I WAS THINKNG
1^(100) vs 2^1. doesn't take much to win!!@@Nick-md9wl
The sound of the chalk hitting the blackboard is magic !!!!!
Simpler solution: 2¹²⁰ = 8⁴⁰ & 3⁹⁰ = 9⁴⁵
Clearly, 9⁴⁵ > 8⁴⁰, so *2¹²⁰ < 3⁹⁰*
You mean 3⁹⁰ >2¹²⁰
You did a slight mistake🫠
@@neelchandra3714 Thnx I rectified it.
Dif btwn JEE Students nd foregeiner! 😂❤
@@patelrudra8179 but the fact that you can't crack any of this.
Wouldn’t it be easier to take the 30th root of both numbers to get, 2^4
Theres a simple approximation i use for exponents. a to the b power = 10 to the (bloga) power. Using that, you can set both exponents at base 10, making them easier to compare. Common formula we use for science olympiad.
Thank you for existing ❤
This problem not important to solve it because my teacher says which one bigger power on number its always small like 2120 or 390 than bigger power of 2120 so its is small 😅 that's it
thank you,sir
3^90 is greater 90= 30×3. 120= 30×4. So it became 27^30 and 16^ 30 so 3^ 90 is greater
Bro has beef with that chalk💀
He forgot to title this "The hardest problem on the ACT test". But otherwise spot on!
Well done, helped me recap a lil
I love this gentlemans math lessons.
I thought it was his biceps RAISED TO THE POWER....
Sir you are extremely wise, Respectfully, NHG
Background sound is very good and great, I cannot comment on it. Wahhhh 😂😅😊
Good one. Alternative 3 = 2^2log3 ~ 1.5 so 3^90 is about 2^135.
?Why is 3 = 2^2log3? Parentheses would make things clearer.
@@paulgoddard7385 i exactly did thisss
Yeah it’s a fooIish comment. I think it only has likes as it introduces another way of thinking, cuz there’s no intelligence in it. Bro’s equality says 3≈1.5 as well 💀
His triceps are getting bigger and my brain is hurting.
No its not easy step we can multiple 2and 120 we get 240 and we can multiple 3 and 90 we get 270 hence we find the answer that which is greater it is easier than your step sir😅😅
The sound reminds me of highschool in the 90s lol
I am wearing a headphone with full media volume and the sound of old white chalk was like slapping someone 😂😂😂😂 .
Sir you don't disappoint
Cool!👍
2^120=8^40
3^90=9^45
now its also easy to see that 3^90 is bigger
Wow ok...😒
My gut feeling was that the 1st one would be WAAAY bigger than the second...😟
Thank you for your great examples.
Another method can be .... Take log of both no. Which ever is greater is ... That no. Is greater
You have great explanations, continue like that, Mansour from Morocco. can i ask you where are you from please?
I was born in South Korea but live in USA.
This would complicate a bit if both exponents were prime numbers.
Probably in that case taking logarythm of both expressions would be the fastest way to compare, but still might need a calculator.
I have a tougher question.
6" or 12"
Which one is bigger?
I would have scored a centum in maths, if he was my teacher in school. Basics are very important and it's in the hands of the teacher to make the subject interesting. I am aged 49 and love all his videos.
Simple clear speech. Good balance between written and spoken. Nice!
he had to solve and explain it within the limit of yt short (a minute max and better less)
No need of this..just use calculator😌🗿
Amazing sir 👍👍
Sir u can directly multiply by upper digit and then add 0
He could have used binomial theorem but this is easy for middle schoolars
this teacher is JACKED
Bro was slanging chalk 😂😂😂
I watched your other video so i can now do this , thanks !
Awe, that was genius!
I love it. Thank you.
Reminds me of my school friends :)..
Easy Alternative way
2^120 3^90
2^3*40 3^2*45
6^40 6^45
2^120 < 3^90
Or just, ya know... put it in the darn calculator....
Without watching the video:
a^b = x can be rewritten to ln x = b*ln a.
Since log is monotonic this operation keeps the relation. At least no arithmetic overflow anymore.
Question now is if 120/90 = 4/3 > ln 3 / ln 2 or same way back 2^4 = 16 > 3^3 = 27.
Well, same as in the video - factoring out gcd of exponent.
Both have number and power(we need to find which is bigger) 'in short cut multiple numbers with power-( 2×120=240) and (3×90=270)' hence 3⁹⁰ is great.it is very easy known?????
Thanks man i really struggled in math but your videos are helping me understand better God bless you
Mesmerised by the chalk - writes so smooth!!
That's one strong chalk
It is Japanese chalk which is very smoothy and doesn't break easily like the other chalks
I just multiplied
2×120 = 240
3×90 = 270
Hence, 270>240
Idk if this will work in other problems as well!
you aren't supposed to multiply by 120 or 90
What if its not possible to convert the base as same...
Top teacher!!
In my country, we memorize log_10(2) and log_10(3). 0.301… and 0.4771 respectively.
2^120 > 120*0.3 = 36
3^90 < 90*0.5 = 45
One is much larger. And we’re dealing with logs! So I think it’s safe to assume 3^90 >
Asians got very good skill at maths😄😄😀
We can also take log on both sides and then calculate
Thank you, Sir😊
I was told there would be no Math.
Not sure when this will become useful for me but I'll definetly use this method when the time comes
Can you do it where you turn the bases the same?
(2⁴)^30 &( 3³)^30 , so 27³⁰ > 16³⁰.
First using the calculator and answer 2nd one is bigger😅
Thank you so much.Excellent teaching,I liked that you used chalk.That’s what my teachers used in those days.Iloved the sound when the chalked talked with the blackboard.Nut there was some noise in the background like carpentry work.However your video is good and I am subscribed.Youtoube recommended it to me .Thanks a zillion.
Take logarithm both side and solve
Which is bigger- your arm muscle😂
No one .... Literally no one
Me seeing his biceps
Thanks for sharing Man !
That was way better. I did this
(2^120)/(3^90)
=(2^30)((2/3)^90)
=(2^30)((4/9)^45)
Very good. Your explanation is PERFECT.
i like this method way easier than what i thought of (and did). i went with the logarithm method
I was thinking about using logarithms.
I have a better technique but I don’t know if it counts :
2^120, u multiplied 2 by 6 and divide the exposant by 6 = 12^20
3^90 same but by 4 = 12^22,5
So 3^90 is higher
3^90=
8727963568087712425891397479476727340041449 (tredecillion)
2^120=
one undecillion, three hundred and twenty-nine decillion, two hundred and twenty-eight nonillionth
Therefore,
2^120
Sorry but the conclusion „and because base 16 is less than 30“ to „so 16^30 is less than 27^30“ is just mathematically nonsense. (-27)^30 is greater than (-16)^30 and -30
sir please solve jee advance questions
Awesome