Pregunta
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( x = \frac{e^5}{20} \)
Solución
Solve the equation \( \ln(4x)+\ln(5)=5 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\ln{\left(4x\right)}+\ln{\left(5\right)}=5\)
- step1: Find the domain:
\(\ln{\left(4x\right)}+\ln{\left(5\right)}=5,x>0\)
- step2: Add the terms:
\(\ln{\left(20x\right)}=5\)
- step3: Convert the logarithm into exponential form:
\(20x=e^{5}\)
- step4: Divide both sides:
\(\frac{20x}{20}=\frac{e^{5}}{20}\)
- step5: Divide the numbers:
\(x=\frac{e^{5}}{20}\)
- step6: Check if the solution is in the defined range:
\(x=\frac{e^{5}}{20},x>0\)
- step7: Find the intersection:
\(x=\frac{e^{5}}{20}\)
The solution to the equation \( \ln 4x + \ln 5 = 5 \) is \( x = \frac{e^5}{20} \).
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Mind Expander
To solve the equation \( \ln 4x + \ln 5 = 5 \), you can combine the logarithms on the left side using the property \( \ln a + \ln b = \ln(ab) \). This gives you: \[ \ln(4x \cdot 5) = \ln(20x) \] Next, set this equal to 5: \[ \ln(20x) = 5 \] To eliminate the natural logarithm, exponentiate both sides by \( e \): \[ 20x = e^5 \] Now, solve for \( x \): \[ x = \frac{e^5}{20} \] And that's your final solution!
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