Conquer Exponential Equations: Math Olympiad Edition | Simple Tips & Techniques

Conquer Exponential Equations: Math Olympiad Edition | Simple Tips & Techniques
"Unlock the secrets to conquering exponential equations in this Math Olympiad Edition tutorial! We'll walk you through simple tips and techniques that will make solving these equations a breeze. Whether you're preparing for a competition or just looking to improve your math skills, this video is perfect for you. Don't miss out on these valuable insights – watch now and become an exponential equation master!

🔹 Key Topics Covered:
- Understanding exponential equations
- Step-by-step techniques for solving
- Tips for simplifying complex problems
- Real-world Math Olympiad examples

🚀 Boost your math skills and confidence with our easy-to-follow guide. Subscribe for more math tutorials and tips!

Topics Covered:
Math Olympiad
Algebra Challenge
Exponential Equation
Problem Solving
Math Competition
Algebra Skills
Math Tutorial
Math Education
Math Problem
Math Challenge

9 Key moments of this video:
0:00 Introduction
0:31 Algebraic identity
0:43 Exponent rules
1:51 Solutions from a^b=1 form
4:26 Verifying Solutions
6:41 Logarithm
7:22 Solving logarithmic equation
9:20 Limits at zero
11:25 Graphing

#matholympiad #algebrachallenge #exponentialequations #problemsolving #mathcompetition #AlgebraSkills #mathtutorial #matheducation #mathproblems #mathchallenge #mathtips #algebra

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Thanks for Watching Video!!
@infyGyan ​

[nasrullahhusnan]

x^(x-5)=x^(5-x)
=x^[-(x-5)]
=1/[x^(x-5)]
Multiply both sides by x^(x-5)
[x^(x-5)]²=1
Take the square root and note that x^(x-5)>0 for all real x≠0. Hence
x^(x-5)=1
Note that if x is odd, k=x-5 is even. x^(x-5)=x^k. For x=±1, x^k=(±1)^k=1 as k is even.
For x-5=0 or x=5 then 5^0=1.
Therefore x={±1, 0}
=--> x=5

[ГеоргийПлодущев-сн]

Так как степень с действительным показателем определена только для неотрицательных чисел, запишем х≥0
Теперь рассмотрим случай, когда х=1
1^1-5=1^5-1
1=1
Подходит, пусть х≠1
х^х-5=х^5-х
=>
х-5=5-х
2х=10
х=5
Ответ: 5; 1

[Nikioko]

(x - 5) lgx = (5 - x) lgx

Case 1: x = 1
(- 4) · 0 = 4 · 0
0 = 0

Case 2: x ≠ 1
x - 5 = 5 - x
2x = 10
x = 5

Case 3: x = - 1
(- 1)⁻⁶ = 1 = (- 1)⁶

x₁ = - 1 ∨ x₂ = 1 ∨ x₃ = 5.
𝕃 = {- 1, 1, 5}

[jormungardwe]

The solutions are -1, 0, 1, 5 you forgot the first case that is x=0 which is the first thing you have to consider when doing a negative exponential

[ManirUddinBarbhuiya-eiuc]

Base is equal, so only x-5=5-x. So X=5 is only reasonable result.