Welcome to SciMarvels! In this video, we tackle a math SAT question involving exponential equations and logarithms. Watch as we break down each step to solve the equation 2^(x+3)=3^(x+2). This problem is an excellent example of how understanding exponents and logarithms can simplify complex equations. Join us on this journey of mathematical discovery and enhance your problem-solving skills!
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Key Concepts Covered
• Exponential equations
• Properties of logarithms
• Logarithmic transformations
• Simplifying complex equations
• Step-by-step solution and problem-solving
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Detailed Steps
We begin with the equation: 2^(x+3) = 3^(x+2)
1. Isolate the exponential terms: (2^x * 2^3) = (3^x * 3^2)
2. Divide both sides by the common base raised to xxx: (2^3 * 2) = (3^2 * 3)
3. Simplify the exponents: (2/3)^x = 9/8
4. Take the logarithm of both sides: log((2/3)^x) = log(9/8)
5. Apply the power rule of logarithms: x * log(2/3) = log(9/8)
6. Solve for xxx: x = log(9/8) / log(2/3)
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Learning Outcomes
By the end of this video, you will:
• Understand how to approach and solve exponential equations.
• Gain proficiency in using logarithms to simplify and solve equations.
• Develop problem-solving strategies for math competitions.
• Enhance your ability to follow and replicate detailed mathematical steps.
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Tags
#OlympiadMath #ExponentialEquations #Logarithms #MathTutorial #SciMarvels #MathProblemSolving #MathCompetition #EducationalVideos #LearnMath #STEM #MathChallenge #MathHelp #AdvancedMath #MathConcepts #MathEducation #StepByStepMath #ProblemSolving #Mathematics #MathSkills #MathLearners , 2^(x+3) = 3^(x+2) , Math SAT Exponential Problem , Step-by-step , How to