How to Solve Complex Equations : Exponential and Radical Challenge | Math Olympiad | Tricky Problem

✅ Video Overview
Welcome to SciMarvels! In this video, we tackle a challenging International Math Olympiad (IMO) problem involving complex exponential equations. Watch as we solve the problem step-by-step on paper, providing a clear and detailed explanation without any voiceover. This unique approach allows you to focus entirely on the math and understand the process visually.
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✅ Key Concepts Covered
- Exponential Equations
- Algebraic Manipulations
- Problem-Solving Strategies
- Properties of Exponents and Radicals
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✅ Detailed Steps
We begin with the problem:
Solve for x in the equation: √(2^x √(4^x √(16^x))) = 16.
Rewrite the equation:
√(2^x √(4^x √(16^x))) = 16
Express the radicals in terms of exponents:
√(2^x √((2^2)^x √((2^4)^x))) = 16
Simplify the exponents inside the radicals:
√(2^x √(2^{2x} √(2^{4x}))) = 16
Combine the exponents:
√(2^x √(2^{2x} * 2^{2x})) = 16
√(2^x √(2^{4x})) = 16
Simplify the inner radical:
√(2^x * 2^{2x}) = 16
Combine the exponents again:
√(2^{3x}) = 16
Rewrite the square root as an exponent:
2^{3x/2} = 16
Express 16 as a power of 2:
16 = 2^4
2^{3x/2} = 2^4
Set the exponents equal to each other:
3x/2 = 4
Solve for x:
3x = 8
x = 8/3
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✅ Also you can see:
• How to Simplify Radica...
• How to Solve Radical E...
• How to Solve Radical E...
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✅ Learning Outcomes
By the end of this video, you will:
- Understand how to simplify and solve complex exponential equations.
- Learn to apply properties of exponents and radicals.
- Gain skills in algebraic manipulation and problem-solving strategies.
- Develop a deeper understanding of how to approach and solve advanced math problems.
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✅ Why Subscribe to SciMarvels?
At SciMarvels, we are dedicated to making complex math and physics problems accessible and enjoyable. Our unique approach of solving problems without voiceovers allows you to concentrate solely on the math, fostering a deeper understanding. Subscribe to join a community of learners who are passionate about mastering scientific concepts through clear, step-by-step solutions.
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✅ Tags
#MathOlympiad #ExponentialEquations #MathTutorial #SciMarvels #AdvancedMath #ProblemSolving #MathCompetition #Algebra #MathSkills #LearnMath #MathWithoutVoice #Educational #MathVideos #STEM #ScienceEducation #MathHelp #Mathematics #OlympiadPreparation #HighSchoolMath #MathCompetitions #MathChallenge #MathPractice #MathConcepts #LearningMathematics #MathSolutions #CompetitiveMath #MathExamPrep #ScientificProblems #MathStrategies
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[@yosefsalehi-bh2zy]

Really interesting question... thank you for tickling my mind 😅

[@Sci-Marvels]

Your welcome Yosef! 😃