Exponential TOWER Equation Solved! | Find $x$ in 9 = 3^{4^{(\sqrt{2})^x}}
Автор: Spencer's Academy
Загружено: 2025-12-03
Просмотров: 70
This challenging exponential equation looks complicated because of the nested exponents (a power tower!), but we break it down step-by-step using fundamental algebra and exponent properties.
You'll learn the elegant method of converting everything to a common base to quickly solve for $x$ in the equation 9 = 3^{(4^{(\sqrt{2})^x})}. This method is essential for math competitions and Olympiad-style problems!
Key Steps Covered: Converting all numbers to the common base of 3, then 2. Using the property: if a^b = a^c, then b=c. Simplifying powers of radicals (\sqrt{2} = 2^{1/2}). Can you solve it before the final answer? Let me know your answer in the comments!
#ExponentialEquations #PowerTower #NestedExponents #SolveForX #Algebra #MathOlympiad #MathProblem #MathChallenge #Exponents #Logarithms #CommonBase #MathHacks #CompetitiveMath
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