Pregunta
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( x = -0.5 \)
Solución
Solve the equation \( 0.8^{(2x+1)}=1 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(0.8^{\left(2x+1\right)}=1\)
- step1: Simplify:
\(\left(\frac{4}{5}\right)^{2x+1}=1\)
- step2: Write in exponential form:
\(\left(\frac{4}{5}\right)^{2x+1}=\left(\frac{4}{5}\right)^{0}\)
- step3: Set the exponents equal:
\(2x+1=0\)
- step4: Move the constant to the right side:
\(2x=0-1\)
- step5: Remove 0:
\(2x=-1\)
- step6: Divide both sides:
\(\frac{2x}{2}=\frac{-1}{2}\)
- step7: Divide the numbers:
\(x=-\frac{1}{2}\)
The solution to the equation \(0.8^{(2x+1)}=1\) is \(x=-\frac{1}{2}\) or \(x=-0.5\).
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Mind Expander
To solve the equation \( 0.8^{(2 x+1)}=1 \), we first recognize that any number raised to the power of 0 equals 1. Thus, we can rewrite our equation as: \[ 2x + 1 = 0 \] Next, we can solve for \( x \): 1. Subtract 1 from both sides: \[ 2x = -1 \] 2. Divide by 2: \[ x = -\frac{1}{2} \] So the solution for \( x \) is: \[ \boxed{-\frac{1}{2}} \]

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