Love Reed
12/11/2023 · Elementary School
c) \( 2^{x}=9 \)
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Step-by-step Solution
Para resolver la ecuación \( 2^{x} = 9 \), podemos tomar el logaritmo en ambos lados. Usaremos el logaritmo en base 10 o el logaritmo natural, dependiendo de tu preferencia. Aquí usaremos el logaritmo natural:
1. Tomamos el logaritmo natural de ambos lados:
\[
\ln(2^{x}) = \ln(9)
\]
2. Usamos la propiedad de los logaritmos que dice que \(\ln(a^b) = b \cdot \ln(a)\):
\[
x \cdot \ln(2) = \ln(9)
\]
3. Despejamos \(x\):
\[
x = \frac{\ln(9)}{\ln(2)}
\]
4. Ahora, podemos calcular el valor numérico:
\[
x \approx \frac{2.1972}{0.6931} \approx 3.17
\]
Por lo tanto, la solución de la ecuación \( 2^{x} = 9 \) es aproximadamente \( x \approx 3.17 \).
Quick Answer
La solución de \( 2^{x} = 9 \) es aproximadamente \( x \approx 3.17 \).
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