How to Solve (18^x+9^x)/(6^x+3^x)=3 Exponential Equations | Math Tricks Shots

In this video, we tackle a challenging exponential equation step-by-step, ensuring you master the techniques required to solve such problems. Our approach is voice-free, focusing purely on visual learning for a clearer understanding.
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Key Concepts Covered:
1. Exponent Rules:
o Applying properties of exponents to simplify and solve equations.
2. Algebraic Manipulation:
o Factorizing expressions to simplify complex equations.
o Using substitution and exponentiation techniques.
3. Step-by-Step Problem Solving:
o Detailed breakdown of each step to ensure a thorough understanding.
o Combining and simplifying expressions efficiently to isolate x.
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Detailed Steps:
1. Initial Equation Analysis:
o Start with the given equation: (18^x−9^x)/(6^x-3^x)=3.
o Recognize and rewrite the bases using prime factorization: 18=2×9 and 6=2×3.
2. Simplify Using Exponents:
o Rewrite the equation in terms of 2^x and 3^x for easier manipulation.
o Substitute and simplify the expressions accordingly.
3. Factorize and Solve:
o Factorize the numerator and denominator to simplify the equation.
o Apply exponent rules to further reduce and solve for x.
4. Verify Solutions:
o Check the solutions by substituting back into the original equation.
o Confirm the correct value of x.
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Learning Outcomes:
By the end of this video, you will:
• Understand how to manipulate and simplify equations involving exponents.
• Be able to apply exponent rules to factorize and solve complex algebraic expressions.
• Gain confidence in breaking down and solving intricate math problems step-by-step.
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• Visual Learning Focus: Enhance your understanding through clear, visual explanations without voiceovers.
• Engaging and Fun: Our unique approach makes learning math enjoyable and interesting.
• Comprehensive Content: We cover a wide range of math and physics topics, providing detailed explanations and step-by-step solutions.
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At SciMarvels, we believe in making learning both fun and effective. By focusing on visual problem-solving without voiceovers, we ensure that you can fully concentrate on the solution process, improving your comprehension and retention of the material.
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Tags:
Exponential Equations, Algebra, Math Tutorials, Educational Math Videos, Fun Learning, SciMarvels Channel, Math Without Voiceover, Visual Learning, Exponent Rules, Algebraic Simplification, KZbin Math, Math Education, Algebra Techniques, Interactive Math, Science and Math Fun, Algebraic Solutions, Silent Math Tutorial, Educational Content, (18^x−9^x)/(6^x-3^x)=3

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