Math Olympiad Challenge: Exponential Problem Solved Without a Calculator

Math Olympiad Challenge: Exponential Problem Solved Without a Calculator | Geendle

Рет қаралды 1,119

Күн бұрын

Hello friends! Welcome to Geendle!
Please kindly ask for your signature. You help me a lot.
In this video I solve an exponential without calculator a calculator.
#squareroot ,#crossmultiplicationmethod ,#division ,#fraction ,#maths ,#algebra ,#subtraction ,#calculus , #Math, #mathematics , #Algebra, #Geometry, #Calculus, #Trigonometry, #statistics , #probability , #linearalgebra , #numbertheory , #Topology, #mathproblems , #mathhelp , #mathtutorial , #MathLessons, #MathEducation, #MathTeacher, #mathstudent , #MathFun, #MathPuzzle, #mathhistory , #mathexplained , #MathForKids, #MathChallenge, #mathisfun
This comprehensive list covers a wide range of topics that can be addressed in math-related content.
Algebra:
Equations
Inequalities
Polynomials
Functions
Systems of Equations
Exponential and Logarithmic Functions
Geometry:
Euclidean Geometry
Coordinate Geometry
Trigonometry
Geometric Transformations
Solid Geometry
Geometric Proofs
Calculus:
Limits
Derivatives
Integrals
Differential Equations
Multivariable Calculus
Sequences and Series
Statistics and Probability:
Descriptive Statistics
Inferential Statistics
Probability Theory
Random Variables
Probability Distributions
Hypothesis Testing
Linear Algebra:
Vectors
Matrices
Determinants
Eigenvalues and Eigenvectors
Vector Spaces
Linear Transformations
Number Theory:
Divisibility
Prime Numbers
Modular Arithmetic
Diophantine Equations
Cryptography
Fermat’s and Euler’s Theorems
Discrete Mathematics:
Combinatorics
Graph Theory
Logic
Set Theory
Algorithms
Boolean Algebra
Topology:
Topological Spaces
Continuity
Compactness
Homotopy
Fundamental Group
Manifolds
Functional Analysis:
Banach Spaces
Hilbert Spaces
Linear Operators
Normed Spaces
Spectral Theory
Fourier Analysis
Mathematical Logic:
Propositional Logic
Predicate Logic
Model Theory
Proof Theory
Set Theory
Computability Theory
Abstract Algebra:
Groups
Rings
Fields
Modules
Galois Theory
Homomorphisms
Applied Mathematics:
Numerical Analysis
Optimization
Differential Equations
Mathematical Modeling
Control Theory
Game Theory
Recreational Mathematics:
Puzzles
Magic Squares
Mathematical Games
Mathematical Paradoxes
Mathematical Art
Fractals
History of Mathematics:
Ancient Mathematics
Medieval Mathematics
Renaissance Mathematics
Modern Mathematics
Biographies of Mathematicians
Development of Mathematical Theories
Mathematics in Computing:
Algorithms
Data Structures
Computational Complexity
Cryptography
Information Theory
Machine Learning
Mathematics in Natural Sciences:
Mathematical Physics
Mathematical Biology
Mathematical Chemistry
Environmental Mathematics
Financial Mathematics
Actuarial Science
Exam Preparation:
SAT Math
ACT Math
GRE Math
GMAT Math
Math Olympiad
College Entrance Exams
Thanks for visiting!

Пікірлер: 26

@davidbrisbane7206 3 ай бұрын

The function in a on the LHS is an ever increasing function as it goes to infinite where a ≥ 1. The difference keeps increasing and starting at a = 1, then the LHS of the equation equals 1. We now know there is one and only one real solution to the LHS = 175. By observation, we see that a = 4 is the one and only solution where a is greater than 1.

@frenchmarty7446 3 ай бұрын

a = 4 Now let's see if I'm right.

@pavelushakov5078 3 ай бұрын

It's easy and now proof that there are no other solutions

@davidbrisbane7206 3 ай бұрын

😂

@Geendle 2 ай бұрын

Yesh! you are!

@pavelushakov5078 3 ай бұрын

Why it's assumed that a is intiger? I don't recall that it was mentioned. Without this assumpton this proof is wrong.

@defhermann 3 ай бұрын

Not really

@Geendle 2 ай бұрын

"a" must be an integer for this problem. I forgot to mention or write in the thumbnail. Thanks for remember.

@defhermann 2 ай бұрын

@@Geendle but isn't it implied that a is an integer by the setup given that we most likely won't get to 175 if the bases are integers?

@Facedfrog 3 ай бұрын

I tried to calculate using the 5x35 and it yield different result, i was wondering how you managed to know it was 7 x 25 that has the correct answer ? Is it hit or miss or did you take the multiplication with the least difference

@Geendle 2 ай бұрын

The factors of 175 that lead us to a positive integer solution are just 7 and 25. The others are not.

@gontusandeep2972 3 ай бұрын

But 'a' doesn't have to be an even number. So, we cannot resolve it as a/2 *2 in the exponent.

@frax5051 3 ай бұрын

Elaborate

@gontusandeep2972 3 ай бұрын

@@frax5051 this same method could not be applied to this question : a^a - (a-1)^a = 2101 the answer is a = 5. Prime factors of 2101 are 11, 191. But if you use the above method you can't get the answer because a is odd integer. The above method assumed a to be an even number even before finding it.

@defhermann 3 ай бұрын

@@gontusandeep2972 I'm getting 7 tho

@Geendle 2 ай бұрын

"a" must be an integer for this problem. I forgot to mention or write in the thumbnail. Thanks for reminding me.

@gontusandeep2972 2 ай бұрын

@@Geendle for the above method doesn't it need to be an even integer