The Shocking Exponential Problem Solving Trick You Never Knew

#exponentialequations #exponentialfunctions #exponential
✅ Video Overview
Welcome to SciMarvels, where we delve into complex mathematical equations and solve them step-by-step. In this video, we analyze an exponential equation involving logarithms and roots. Follow along as we explore the algebraic manipulation needed to solve for x, making it easy to understand and apply. This video is perfect for students preparing for advanced math exams or anyone interested in deepening their understanding of exponential equations.
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✅ Key Concepts Covered
• Exponential equations
• Logarithms
• Algebraic manipulation
• Quadratic equations
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✅ Detailed Steps
1. Given: 10^x + 100^x = 1000^x, Find x
2. Rewrite the equation using powers of 10
10^x + (10^2)^x = (10^3)^x
10^x + (10^x)^2 = (10^x)^3
3. *Let t = 10^x*
t + t^2 = t^3
4. Rearrange to form a cubic equation
t^3 - t^2 - t = 0
5. Factor the cubic equation
t(t^2 - t - 1) = 0
6. Solve the quadratic part using the quadratic formula
t = [1 ± √5] / 2
7. Analyze the solutions
For t = 0: 10^x = 0 (Not possible)
For t = (1 - √5) / 2 : 10^x is negetaive (Not possible)
For t = (1 + √5) / 2: 10^x is positive (Valid)
8. Final answer
x = log[(1 + √5) / 2]
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✅ Tags:
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[@yosefsalehi-bh2zy]

God bless you i was looking for this exact thing

[@Sci-Marvels]

Thanks Yosef ☺️