Solving Exponential Equations Unraveling 2024

<ul> <li> Solving Exponential Equations Unraveling a Math Olympiad Problem </li> </ul>

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

The equation is presented as 3^(sqrt(x) / 2) = 3^(1 / sqrt(x).
To solve for x, the video simplifies the equation.
The first step involves rewriting the equation as 3^(sqrt(x)) / 2 = 3^(1 / sqrt(x).
Using the property that a^(n) = a^(m) implies n = m, the video establishes that sqrt(x) / 2 = 1 / sqrt(x).
Now, we cross multiply to obtain sqrt(x) * sqrt(x) = 2.
This leads to the equation sqrt(x)^2 = 2, and subsequently, x = 2.
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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