Pregunta
Write the logarithmic equation in exponential form. For example, the exponential form of \( \log _{5}(25)=2 \) is \( 5^{2}= \) \[ \log _{32}(4)=\frac{2}{5} \]
Ask by Summers Carrillo. in the United States
Jan 23,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The exponential form of \( \log_{32}(4) = \frac{2}{5} \) is \( 32^{\frac{2}{5}} = 4 \).
Solución
To convert the logarithmic equation \( \log_{32}(4) = \frac{2}{5} \) into its exponential form, you can use the definition of a logarithm:
\[
\log_{b}(a) = c \quad \text{is equivalent to} \quad b^{c} = a
\]
Applying this to your equation:
\[
\log_{32}(4) = \frac{2}{5} \quad \Rightarrow \quad 32^{\frac{2}{5}} = 4
\]
**Exponential Form:**
\[
32^{\frac{2}{5}} = 4
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
Como
error msg
Explicar 
Simplifique esta solución Mind Expander
To rewrite the logarithmic equation \(\log_{32}(4) = \frac{2}{5}\) in exponential form, we can apply the definition of a logarithm. This means that if \(\log_b(a) = c\), then it can be rewritten as \(b^c = a\). So, transforming \(\log_{32}(4) = \frac{2}{5}\) into exponential form gives us: \[ 32^{\frac{2}{5}} = 4. \] This equation tells us that raising 32 to the power of \(\frac{2}{5}\) will yield 4!
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
