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- เผยแพร่เมื่อ 2 ก.ค. 2024
- A Nice Factorial Exponential Equation | Olympiad Math Prep!
Get ready to tackle an intriguing factorial exponential equation in this Olympiad Math Prep video! Perfect for those preparing for math competitions or anyone looking to sharpen their problem-solving skills. Join us as we break down this challenging equation step-by-step, providing you with valuable insights and techniques to solve similar problems.
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Topics covered:
Exponential equations
Factorial
Factorial laws
How to solve exponential equations?
Algebra
Properties of exponents
Algebraic identities
Radicals
Positive Integers
Factorial Exponential Equation
Math Olympiad preparation
Math Olympiad training
Exponent laws
Real solutions
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Thanks for Watching !!
X!^(x+1)!= 24^ 120
Hence; x= 4
I have got the right answer.
X=4
The RHS = 16^(18). 9^(12) = 24^24 = (4!)^(4!) THUS, (X!)^(X+1!) = (4!)^(4! . 5) = (4!)^(5!). THUS, X = 4.
[x!^x!]^(x+1)=[(24)^(24)]^5 αρα x+1=5 , x=4
sqrt(16³⁶)=16¹⁸
=8¹⁸2¹⁸
=8¹⁸(2³)⁶
=8²⁴
cbrt(9³⁶)=9¹²=3²⁴
[sqrt(16³⁶)][cbrt(9³⁶)=8²⁴3²⁴
=24²⁴
(x!)^(x+1)!=(24²⁴)⁵
=24¹²⁰
=(4!)^[5(4!)]
=4!^(5!)
=4!^(4+1)! --> x=4
5x^10 5^1x^2^5 1^1x2^1; x^2^1 ( x ➖ 2x+1) 32^72 4^16^8^9 4^4^4^8^3^2 2^22^22^2^2^3^3^2 1^11^11^11^12^13^1 23 (x ➖ 3x+2) 27^118 3^9^10^10^8 3^3^3^2^52^52^3 1^1^31^11^12^1 32 (x ➖ 3x+2)
Πραγματικα εισαι ο νεος αινσταιν
Seems quite easy for JEE or Olympiads.
X=4