✅ Video Overview
Welcome to SciMarvels, where complex math problems are simplified and solved with ease. In this video, we delve into solving the equation 7^(x+8) = 8^(x+7). Watch as we break down the problem step-by-step, using algebraic manipulation and logarithms to find the value of x. Join us and enhance your understanding of mathematical problem-solving techniques.
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✅ Key Concepts Covered
• Algebraic manipulation
• Properties of exponents
• Using logarithms
• Simplifying complex equations
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✅ Detailed Steps
1. *Given: 7^(x+8) = 8^(x+7)*
7^(x+8) = 7^x * 7^8
8^(x+7) = 8^x * 8^7
2. *Divide both sides by 8^7 and 7^8*
(7/8)^x * 7^8 / 8^7 = 1
3. *Using logarithms to solve for x*
log((7/8)^x) = log((8/7)^7)
x * log(7/8) = log((8/7)^7)
4. *Simplify the logarithmic equation*
x = log((8/7)^7) / log(7/8)
x = 7 * log(8/7) / log(7/8)
5. *Final step*
x = (7 * log 8 - 8 * log 7) / (log 7 - log 8)
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✅ Learning Outcomes
By the end of this video, you will:
• Understand how to manipulate and simplify complex exponential equations.
• Be able to apply logarithms effectively.
• Gain confidence in solving complex mathematical problems step-by-step.
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✅ Why Subscribe to SciMarvels?
At SciMarvels, we simplify complex scientific concepts and make learning an enjoyable experience. Subscribe to our channel to access:
• Clear and concise problem-solving videos.
• A wide range of topics in physics and mathematics.
• Interactive and engaging learning methods.
• Regular content updates to keep you ahead in your studies.
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✅ Tags:
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