Pregunta
1 of 5 Solve for \( x: 3^{2 x-1}=27 \). (1 point) 1 2
Ask by Watson Black. in the United States
Mar 14,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( x = 2 \)
Solución
1. Rewrite the equation by expressing \(27\) as a power of \(3\):
\[
27 = 3^3
\]
2. Substitute into the equation:
\[
3^{2x-1} = 3^3
\]
3. Since the bases are equal, set the exponents equal to each other:
\[
2x - 1 = 3
\]
4. Solve for \(x\):
\[
2x = 3 + 1 = 4
\]
\[
x = \frac{4}{2} = 2
\]
Thus, the solution is \(x = 2\).
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución Beyond the Answer
To solve for \( x \) in the equation \( 3^{2x-1} = 27 \), we start by expressing 27 as a power of 3. Since \( 27 = 3^3 \), we can rewrite the equation as \( 3^{2x-1} = 3^3 \). Now that the bases are the same, we can set the exponents equal to each other: \[ 2x - 1 = 3 \] Next, we solve for \( x \): 1. Add 1 to both sides: \[ 2x = 4 \] 2. Divide by 2: \[ x = 2 \] So, the solution is \( x = 2 \).
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
