This Math Problem Baffled Everyone | One of the Trickiest Mathematics Questions
Вставка
- Опубліковано 28 тра 2024
- What is a correct answer? What do you think about this problem?
Check out my latest video: • Can You Pass Harvard's...
Thank You for everything! If you're reading this ❤️.
Hello My Friend ! Welcome to my channel. I really appreciate it!
@higher_mathematics
#maths #algebra #math #olympiad
Isn’t it simpler to give the answer as 3 ^9^9
Yes but thats simpler and better but it's not on there. You need to recognise that d is the same as this
I think it would be easier to write 9 to the 9th to the 4.5th. If you are going to divide the exponent by the base of the radical then you divide the upper 9 by 2, the other two 9s are unaffected. You could even write it as 9 to the 9th in parentheses and put the last 9 on the outside of the parentheses.
4,43426^38 (15 sec) 😀
Your 9 looks like a g.. Excellent channel Thank you
Nice!!! Gravias!!!
Why write 'g' if you mean '9'?
9^9^9^(0.5)=9^9^3. Power towers are evaluated from the top down.
You're right and wrong:
Yes the stack is evaluated 9^(9^9), but what you're evaluating is the square root of the whole thing, i.e.:
(9^(9^9))^0.5
= 9^(0.5*(9^9))
= 9^(0.5*9*(9^8))
= 9^(4.5*(9^8))
Also 3^(9^9) would work but that's not on there
What does the power of a fraction even mean? like, 10^2 is 10 times 10.
But 10^(1/2) is the root and 2^(0.3333...)? What are those notation describing?
How can it be multiplied with itself partially?
It's a weird concept but partially you can think about rational powers as taking the integer power of the numerator and taking the denominator'th root. A little weirder when the power is irrational but there are continuations you can do
Specifically to your question 2^0.3333... means the principal cube root of 2
@@DanDartI think that this might be a very good way of conceptualizing it. Thank you for the answer !
2^(.333...) = 2^(1/3) -> What number mutiplied 3 times is equal to 2
ex 9^(1/2) -> what nuber mutiplied 2 times makes nine, aka root of ...
A^(1/N) -> what number multiplied B times makes A, aka N:th root of
ex 81^(1/4) = 3 * 3 * 3 * 3 , 3 multiplied 4 times...
Thers a relationship with Logarithmic functions...
Log base ten (on most calculors), ask the question how many times must the number 10 be multiplied to make the value, in a more general term log can have any base (even fractions)
..by using log base rules we can write for example
Log base 3(81) as Log(81)/Log(3) and the answer is 4 ... we need to multiply 3 four times to get 81
Log base rule: LogA(B) = LogX(B)/LogX(A); X is an arbitrary log base
ex: 3^B = 81-> B = Log(81)/Log(3) = 4 (4:th root of 81 is 3, or 81^(1/4) = 3)
ps. on most caculators it just say 'Log' wich is Log base 10, Log base 2 is also quite common as it relates to binary (two digits 1 and 0)...
@Higher Matematics The result is inaccurate, 3^81 is correct. I did the test and it is correct!!!!!
No it isn't!!!!!. If you square 3 ^ 81 you get 9 ^ 81 which is 9 ^ ( 9 * 9 ) which is a tiny tiny splinter compared to 9 ^ ( 9 ^ 9 ). What was the test by the way?
I get the same answer. 9^(81/2) = 3^81
@@tambourineman17 Where does the 81 come from? 9^9 is a lot bigger than 9x9
obviously it is 9^((9^9)/2). simple enoug. the answers are also obviously in ascending order. 9^3 is obviously less than (9^9)/2. answer is d
Write sentences.
This question is nothing compared to what i have solved, i have solved much much more difficult questions in my regular 12th standard class while preparing for JEE ADVANCED