Rewrite each equation as requested.
(a) Rewrite as a logarithmic equation.
\[
e^{y}=7
\]
(b) Rewrite as an exponential equation.
\[
\ln x=9
\]

Step 1 ：Rewrite each equation as requested.

Step 2 ：For part (a), we have the exponential equation \(e^{y}=7\). To rewrite this as a logarithmic equation, we need to understand that the base of the logarithm will be the base of the exponential, which is \(e\) in this case. The argument of the logarithm will be the right side of the equation, which is \(7\). The result of the logarithm will be the exponent in the exponential equation, which is \(y\).

Step 3 ：For part (b), we have the logarithmic equation \(\ln x=9\). To rewrite this as an exponential equation, we need to understand that the base of the exponential will be \(e\) because \(\ln\) is the natural logarithm, which is base \(e\). The exponent will be the right side of the equation, which is \(9\). The result of the exponential will be the left side of the equation, which is \(x\).

Step 4 ：Final Answer: \(\boxed{\text{(a) The exponential equation } e^{y}=7 \text{ can be rewritten as a logarithmic equation as } \ln 7 = y.}\)

Step 5 ：Final Answer: \(\boxed{\text{(b) The logarithmic equation } \ln x=9 \text{ can be rewritten as an exponential equation as } x = e^{9}.}\)