Rewrite each equation as requested. (a) Rewrite as an exponential equation. \[ \ln 4=y \] (b) Rewrite as a logarithmic equation. \[ e^{x}=7 \]

Step 1 ：Rewrite each equation as requested.

Step 2 ：(a) The equation \(\ln 4=y\) is a logarithmic equation with base \(e\). To rewrite it as an exponential equation, we need to remember that the logarithm base \(b\) of a number \(x\) is the exponent to which \(b\) must be raised to produce \(x\). So, we can rewrite the equation as \(e^{y}=4\).

Step 3 ：(b) The equation \(e^{x}=7\) is an exponential equation with base \(e\). To rewrite it as a logarithmic equation, we need to remember that the logarithm base \(b\) of a number \(x\) is the exponent to which \(b\) must be raised to produce \(x\). So, we can rewrite the equation as \(\ln 7=x\).

Step 4 ：Final Answer:

Step 5 ：(a) The exponential form of the equation \(\ln 4=y\) is \(\boxed{e^{y}=4}\).

Step 6 ：(b) The logarithmic form of the equation \(e^{x}=7\) is \(\boxed{\ln 7=x}\).