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solve for \( x \) 1) \( 3^{x}-3^{x-2} \)

Ask by Huff Salazar. in South Africa
Jan 29,2025

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The equation \(3^{x} - 3^{x-2} = 0\) has no real solutions for \(x\).

Solución

The provided equation is not in the correct format for solving. Let's rewrite the equation as \(3^x - 3^{x-2} = 0\) and then solve for \(x\). Solve the equation by following steps: - step0: Solve for \(x\): \(3^{x}-3^{x-2}=0\) - step1: Subtract the terms: \(8\times 3^{x-2}=0\) - step2: The statement is false for any value of \(x:\) \(x \notin \mathbb{R}\) The equation \(3^x - 3^{x-2} = 0\) does not have any real solutions for \(x\).

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The Deep Dive

To solve the equation \( 3^{x}-3^{x-2} = 0 \), start by factoring out the common term. We can rewrite \( 3^{x-2} \) as \( \frac{3^x}{9} \): \[ 3^{x} - \frac{3^{x}}{9} = 0. \] This simplifies to: \[ 3^{x} (1 - \frac{1}{9}) = 0. \] Now simplify the expression in the parentheses: \[ 1 - \frac{1}{9} = \frac{8}{9}. \] So we have: \[ 3^{x} \cdot \frac{8}{9} = 0. \] Since \( 3^{x} \) cannot be zero (as it is an exponential function), we can conclude that there is no value of \( x \) that satisfies this equation. Therefore, this equation has no solutions.

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