How to Solve 8^x + 8^x = 8 | SAT Math Problem | Magic Tricks | Mathematic Exam Preparation

✅ In this session, we solve the equation 8^x + 8^x = 8. We will break down the problem step-by-step, utilizing properties of exponents and algebraic manipulations to find the value of x. This tutorial is ideal for students preparing for exams, math enthusiasts, and anyone looking to deepen their understanding of exponential equations.
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✅ Key Concepts Covered:
1. Properties of Exponents:
Applying exponent rules.
Simplifying exponential expressions.
2. Algebraic Techniques:
Working with algebraic identities.
Solving polynomial equations.
3. Problem Solving Strategies:
Breaking down complex problems into manageable steps.
Logical progression from problem statement to solution.
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✅ Detailed Steps:
Problem:
8^x + 8^x = 8
Step 1: Express 8 in terms of its prime factors:
8 = 2^3
Step 2: Substitute the prime factorization into the equation:
(2^3)^x + (2^3)^x = 8
2^(3x) + 2^(3x) = 8
Step 3: Let t = 2^x, then the equation becomes:
t^3 + t^3 = 8
2t^3 = 8
Step 4: Simplify the equation:
t^3 = 8 / 2
t^3 = 4
t^3 = 2^2
Step 5: Taking the cube root of both sides:
(t^3)^(1/3) = (2^2)^(1/3)
t = 2^(2/3)
Step 6: Recall t = 2^x, so we have:
2^x = 2^(2/3)
Step 7: Since the bases are the same, equate the exponents:
x = 2/3
Thus, the solution is:
x = 2/3
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✅ Learning Outcomes:
By the end of this video, you will:
• Understand how to manipulate and simplify exponential expressions.
• Be able to apply algebraic techniques to solve exponential equations.
• Gain confidence in solving algebraic problems step-by-step.
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✅ Also you can see:
   • Math Olympiad EXPERT Reveals Simple S...  
   • How to Solve Complex Equations : Expo...  
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