Solving Exponential Equations Unraveling A Math Olympiad Problem
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- Explore the solution to a challenging mathematical problem involving exponentiation. Learn how to find the value of x that satisfies the equation 3^(sqrt(x) / 2) = 3^(1 / sqrt(x). Join us for an informative journey through this math olympiad challenge.
- The video discusses how to solve a mathematical problem related to exponentiation.
- The equation in question is 3^(sqrt(x) / 2) = 3^(1 / sqrt(x), and the goal is to find the value of x that satisfies it.
In this video tutorial, we delve into a complex mathematical problem that is a part of the Math Olympiad. The problem revolves around solving an equation related to exponentiation. The equation in question is as follows 3^(sqrt(x) / 2) = 3^(1 / sqrt(x). The ultimate goal is to determine the value of x that satisfies this equation. Let's break down the solution step by step
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The equation is presented as 3^(sqrt(x) / 2) = 3^(1 / sqrt(x).
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To solve for x, the video simplifies the equation.
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The first step involves rewriting the equation as 3^(sqrt(x)) / 2 = 3^(1 / sqrt(x).
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Using the property that a^(n) = a^(m) implies n = m, the video establishes that sqrt(x) / 2 = 1 / sqrt(x).
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Now, we cross multiply to obtain sqrt(x) * sqrt(x) = 2.
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This leads to the equation sqrt(x)^2 = 2, and subsequently, x = 2.
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Therefore, the value of x that satisfies the given equation is x = 2.
In summary, this video provides a clear and concise solution to a challenging math problem from the Math Olympiad. By applying mathematical properties and simplifying the equation, the value of x is found to be 2, which satisfies the equation 3^(sqrt(x) / 2) = 3^(1 / sqrt(x).
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