Converting between natural logarithmic and exponential equations Rewrite each equation as requested. (a) Rewrite as an exponential equation. \[ \ln x=6 \] (b) Rewrite as a logarithmic equation. \[ e^{9}=y \] (a) $\square$ (b)

Step 1 ：Given the equation \(\ln x = 6\), we can rewrite it in exponential form as \(e^6 = x\).

Step 2 ：Calculating \(e^6\), we find that \(x \approx 403.43\).

Step 3 ：Given the equation \(e^9 = y\), we can rewrite it in logarithmic form as \(\ln y = 9\).

Step 4 ：Calculating \(e^9\), we find that \(y \approx 8103.08\).

Step 5 ：Final Answer: \n(a) The exponential form of the equation \(\ln x = 6\) is \(e^6 = x\), which gives \(x \approx \boxed{403.43}\). \n(b) The logarithmic form of the equation \(e^9 = y\) is \(\ln y = 9\), which gives \(y \approx \boxed{8103.08}\).