Pregunta
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\( x=5 \)
Solución
Solve the equation \( 3^{-x}=\frac{1}{243} \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(3^{-x}=\frac{1}{243}\)
- step1: Rewrite in exponential form:
\(3^{-x}=3^{-5}\)
- step2: Set the exponents equal:
\(-x=-5\)
- step3: Change the signs:
\(x=5\)
The solution to the equation \(3^{-x}=\frac{1}{243}\) is \(x=5\).
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución The Deep Dive
To solve the equation \( 3^{-x} = \frac{1}{243} \), you first need to recognize that \( 243 \) can be expressed as a power of \( 3 \). In fact, \( 243 = 3^5 \). Therefore, we can rewrite \( \frac{1}{243} \) as \( 3^{-5} \). Now the equation becomes: \[ 3^{-x} = 3^{-5} \] Since the bases are the same, we can set the exponents equal to each other: \[ -x = -5 \] Solving for \( x \), we get: \[ x = 5 \] Thus, the solution to the equation is \( x = 5 \).
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