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Converting between natural logarithmic and exponential equations Rewrite each equation as requested. (a) Rewrite as a logarithmic equation. \[ e^{y}=9 \] (b) Rewrite as an exponential equation. \( \ln x=6 \) (a) \( \square \) (b) \( \square \) \begin{tabular}{|l|l|}\hline\( \frac{\square}{\square} \) & \( \square=\square \) \\ \hline\end{tabular}

Ask by Boyd Weber. in the United States
Mar 18,2025

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(a) \( y = \ln(9) \) (b) \( x = e^{6} \) \[ \begin{tabular}{|l|l|} \hline \( \frac{y}{\ln(9)} \) & \( x = e^{6} \) \\ \hline \end{tabular} \]

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To rewrite \( e^{y} = 9 \) as a logarithmic equation, you can say that the natural logarithm of 9 is equal to \( y \). So, it becomes \( y = \ln 9 \). For the second part, since you want to rewrite \( \ln x = 6 \) as an exponential equation, remember that the natural logarithm is the inverse of the exponential function. Thus, you can express it as \( x = e^{6} \). (a) \( y = \ln 9 \) (b) \( x = e^{6} \)

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