Pregunta
upstudy study bank question image url

k 3. Chapter 3 (Course Work \( 1 \leftarrow \) Solve the following exponential equation. Express the solution set in terms of natural logarithms or commor \[ 7 e^{2 \mathrm{x}}=1253 \] The solution set expressed in terms of logarithms is \( \{\square\} \). (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any nur

Ask by Rogers Barnett. in Saudi Arabia
Mar 09,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

The solution set is \( x = \frac{\ln(179)}{2} \).

Solución

Solve the equation \( 7e^{2x}=1253 \). Solve the equation by following steps: - step0: Solve for \(x\): \(7e^{2x}=1253\) - step1: Divide both sides: \(\frac{7e^{2x}}{7}=\frac{1253}{7}\) - step2: Divide the numbers: \(e^{2x}=179\) - step3: Take the logarithm of both sides: \(\ln{\left(e^{2x}\right)}=\ln{\left(179\right)}\) - step4: Evaluate the logarithm: \(2x=\ln{\left(179\right)}\) - step5: Divide both sides: \(\frac{2x}{2}=\frac{\ln{\left(179\right)}}{2}\) - step6: Divide the numbers: \(x=\frac{\ln{\left(179\right)}}{2}\) The solution to the exponential equation \(7e^{2x}=1253\) is \(x = \frac{\ln(179)}{2}\). Therefore, the solution set expressed in terms of natural logarithms is \(\left\{\frac{\ln(179)}{2}\right\}\).

Respondido por UpStudy AI y revisado por un tutor profesional

error msg
Explicar
Simplifique esta solución

The Deep Dive

To isolate \( e^{2x} \), start by dividing both sides by 7: \[ e^{2x} = \frac{1253}{7} \] Next, take the natural logarithm of both sides: \[ 2x = \ln\left(\frac{1253}{7}\right) \] Now, divide by 2 to solve for \( x \): \[ x = \frac{1}{2} \ln\left(\frac{1253}{7}\right) \] So the solution set expressed in terms of logarithms is \( \left\{ \frac{1}{2} \ln\left(\frac{1253}{7}\right) \right\} \). For some fun facts: Did you know that the natural logarithm has some super cool applications in fields like biology? For example, they help model population growth, as organisms multiply exponentially. This makes it crucial for ecologists studying sustainable practices. And for those diving deeper into the world of logarithms, exploring "The Joy of x" by Steven Strogatz can be a great start. It beautifully explores mathematical concepts, including those snazzy logarithms, in a way that’s engaging and easy to understand!

preguntas relacionadas

Latest Algebra Questions

¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde Hazte Premium
Estudiar puede ser una verdadera lucha
¿Por qué no estudiarlo en UpStudy?
Seleccione su plan a continuación
Prima

Puedes disfrutar

Empieza ahora
  • Explicaciones paso a paso
  • Tutores expertos en vivo 24/7
  • Número ilimitado de preguntas
  • Sin interrupciones
  • Acceso completo a Respuesta y Solución
  • Acceso completo al chat de PDF, al chat de UpStudy y al chat de navegación
Básico

Totalmente gratis pero limitado

  • Solución limitada
Bienvenido a ¡Estudia ahora!
Inicie sesión para continuar con el recorrido de Thoth AI Chat
Continuar con correo electrónico
O continuar con
Al hacer clic en "Iniciar sesión", acepta nuestros términos y condiciones. Términos de Uso & Política de privacidad