Pregunta
1)) Use properties of logarithms to evaluate the expression. \( \ln e^{12}-\ln e^{8} \)
Ask by Lane Chan. in the United States
Mar 14,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The expression evaluates to 4.
Solución
1. Start with the expression:
\[
\ln e^{12} - \ln e^{8}
\]
2. Use the logarithmic property that \(\ln e^x = x\):
\[
\ln e^{12} = 12 \quad \text{and} \quad \ln e^{8} = 8
\]
3. Substitute these into the original expression:
\[
12 - 8
\]
4. Simplify the result:
\[
4
\]
Thus, the evaluated expression is \(4\).
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución Mind Expander
Let's simplify the expression step-by-step! First, we can use the property of logarithms that states \( \ln a^b = b \cdot \ln a \). So, we can rewrite the expression as: \( \ln e^{12} = 12 \cdot \ln e \) and \( \ln e^{8} = 8 \cdot \ln e \). Since \( \ln e = 1 \), we have: \( 12 \cdot 1 - 8 \cdot 1 = 12 - 8 = 4 \). Thus, the final answer is \( 4 \). Want to spice things up with some exciting facts or applications of logarithms? Just let me know!
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
