Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation \(3^{x} - 3^{x-2} = 0\) has no real solutions for \(x\).
Solution
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 \(x\).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution 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.
