Question
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
Upstudy AI Solution
Tutor-Verified Answer
Answer
(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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Beyond the Answer
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) \( x = e^{6} \)