Solve the nested exponential equation

#Shorts #Math #Maths #PreMath #MathTricks #MathTrick #MathTrickHacks #MathHack #MathHack #short #Exponential #Solve #ExponentialEquations

Solve the nested exponential equation

Mathematics
Algebra
Calculus
Geometry
Trigonometry
Statistics
Graph theory
Number theory
Mathematical analysis
Topology
Logic
Abstract algebra
Combinatorics

[alfonsorodriguez]

This is a special case of x^x^x…..^x^a=a which is just x^a=a. This is easy to prove.
Let x^a=a and let’s show that it is equivalent to x^x^a=a.

So let x^a=a then take x=x which is true and raise it to “a” which gives you x^a=x^a.
Now substitute x^a for the a in the right side of the equation and substitute a for x^a to the left side of the equation to get x^x^a=a. In this problem, a=77 so x^x^77=77 is equivalent to x^77=77 and therefor x=77^(1/77).
In fact, we can keep doing this process and get that x^x^x……..x^a=a is the same as x^a=a which we can then solve.

[abhijitsanyal]

If you take logarithms both side then the solution becomes easier

[EngagingOverImmersive]

I'm guessing this is for indians given the names in the comments, but as an American who likes math this was a very enjoyable video. You have a really soothing voice.

[gdtutorial]

Wai-, did u just made a mistake..?


• x^x^77 = (77)
• √(x^x^77)⁷⁷ = √(77)⁷⁷
• x^x = √(77)⁷⁷ ≠ x

[anshumansingh]

sir can you explian this question by logrithm method

[sy]

​I have a doubt
(aª)​⁷⁷=77
So what the value
You had given the answer one year ago video
So a=77 rod 77
Bue i think it not possible
Because
(aª)⁷⁷*⁷⁷=77⁷⁷
a⁷⁷=77
So before qusetion (aª)⁷⁷=77
So a⁷⁷=aª*⁷⁷
77a=77
a=1
1 can't be there
So Ithink it not possible to
a=77rod77
Can you sendmethe correct answer

[ACheateryearsago]

Wait isn't the question in x to the power of x to the power of 77? So how did you replace the position of 77 and x as if it's in multiplication form?

Like, X^77X≠X^X^77

[noskillman]

About a^a=b^b => a=b
This property is false, look at the graph of x^x and you will see that x^x = c can have two solutions

Edit : It's actually true for c>1, but definitely not trivial

[sy]

If (aª)⁷⁷=a⁷⁷
So 77a=77
a=77÷77
=1
So( 1¹)⁷⁷not =77
How is it possible

[RSR]

Sir, I am very confused in HCF of 0, 6
Some say ans 6 will come and some say ans is not define.
If ans 6 is right ans then it is not proved by by the othe method(division method).
Sir, Big question= What is the factor 0
Sir sir please give me a ans

[GhostT]

*_aᵃ=bᵇ <=> a=b_*
0⁰=2² <=> 0=2 (wrong😂)