Exponent Shortcut You Didn't Know About! Math Olympiad Problem

#matholympiad #exponentialequations #Algebra
✅ Video Overview
Welcome to SciMarvels, where we explore and solve challenging mathematical equations. In this video, we tackle an exponential equation that requires careful manipulation and understanding of powers. Join us as we break down the steps to find the value of x, using algebraic techniques and exponent rules. This video is ideal for students preparing for math competitions or those looking to strengthen their problem-solving skills.
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✅ Key Concepts Covered
• Exponential equations
• Algebraic manipulation
• Properties of exponents
• Solving for unknowns
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✅ Detailed Steps
1. Given: 2^x = x^32, Find x
2. Rewrite the equation by taking the reciprocal of the exponent
(2^x)^(1/x) = (x^32)^(1/x)
3. Simplify the expression
2^(1/32) = x^(1/x)
4. Take the 64th power of both sides
2^(2/64) = x^(1/64)
5. Express the equation in terms of powers of 2
4^(1/128) = x^(1/x)
6. Continue simplifying
16^(1/256) = x^(1/x)
7. Recognize the pattern
(256)^(1/256) = x^(1/x)
8. Final answer
x = 256
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✅ Tags:
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[@francoferrario2869]

Così però perdi almemo una altra soluzione

[@Sci-Marvels]

Grazie per il tuo commento! È vero, ci sono anche altre soluzioni. Questa era solo una proposta.

[@yosefsalehi-bh2zy]

That's literally what shortcut means

[@Sci-Marvels]

Thanks 😊