Pregunta
Question 6 Expand and simplify the logarithm: \( \log _{5}\left(\frac{x^{3}}{25}\right) \).
Ask by Tucker Schneider. in the United States
Mar 19,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( \log_{5}\left(\frac{x^3}{25}\right) = 3\log_{5}(x) - 2 \)
Solución
1. Write the given expression:
\[
\log_{5}\left(\frac{x^3}{25}\right)
\]
2. Apply the logarithm quotient rule:
\[
\log_{5}\left(\frac{x^3}{25}\right) = \log_{5}(x^3) - \log_{5}(25)
\]
3. Use the logarithm power rule for the first term:
\[
\log_{5}(x^3) = 3\log_{5}(x)
\]
4. Notice that \(25 = 5^2\) and apply the logarithm power rule for the second term:
\[
\log_{5}(25) = \log_{5}(5^2) = 2
\]
5. Substitute these back into the expression:
\[
\log_{5}\left(\frac{x^3}{25}\right) = 3\log_{5}(x) - 2
\]
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución The Deep Dive
To expand and simplify the logarithm \( \log _{5}\left(\frac{x^{3}}{25}\right) \), you can use the properties of logarithms. First, apply the quotient rule: \[ \log_{5}\left(\frac{x^{3}}{25}\right) = \log_{5}(x^{3}) - \log_{5}(25) \] Now, simplify each term. For the first term, utilize the power rule: \[ \log_{5}(x^{3}) = 3\log_{5}(x) \] For the second term, since \( 25 = 5^2 \): \[ \log_{5}(25) = \log_{5}(5^2) = 2 \] Putting it all together gives: \[ \log_{5}\left(\frac{x^{3}}{25}\right) = 3\log_{5}(x) - 2 \] Thus, the final answer is: \[ 3\log_{5}(x) - 2 \]
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
