Express each equation in logarithmic form.
(a) $e^{x}=5$ is equivalent to the logarithmic equation:
(b) $e^{7}=x$ is equivalent to the logarithmic equation:

Step 1 ：Express each equation in logarithmic form.

Step 2 ：The general form of an exponential equation is \(b^{y} = x\), where \(b\) is the base, \(y\) is the exponent, and \(x\) is the result. This can be converted into logarithmic form as \(\log_{b}x = y\).

Step 3 ：For the first equation, \(e^{x}=5\), the base is \(e\), the exponent is \(x\), and the result is \(5\). So, the logarithmic form would be \(\log_{e}5 = x\).

Step 4 ：For the second equation, \(e^{7}=x\), the base is \(e\), the exponent is \(7\), and the result is \(x\). So, the logarithmic form would be \(\log_{e}x = 7\).

Step 5 ：Note that \(\log_{e}\) is also represented as \(\ln\).

Step 6 ：\(\boxed{\text{Final Answer:}}\)

Step 7 ：(a) The logarithmic form of \(e^{x}=5\) is \(\boxed{\ln5 = x}\) or \(\boxed{\log_{e}5 = x}\).

Step 8 ：(b) The logarithmic form of \(e^{7}=x\) is \(\boxed{\ln x = 7}\) or \(\boxed{\log_{e}x = 7}\).