Express equation equation in logarithmic form.
(a) $e^{x}=5$ is equivalent to the logarithmic equation:
(b) $e^{4}=x$ is equivalent to the logarithmic equation:

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Step 1 ：Express the given exponential equations in logarithmic form.

Step 2 ：For the first equation, \(e^{x}=5\), express it in logarithmic form as \(\log_{e}5=x\).

Step 3 ：Since the base \(e\) is the natural logarithm, simplify it further as \(\ln5=x\).

Step 4 ：For the second equation, \(e^{4}=x\), express it in logarithmic form as \(\log_{e}x=4\).

Step 5 ：Again, since the base \(e\) is the natural logarithm, simplify it further as \(\ln x=4\).

Step 6 ：Final Answer: (a) The logarithmic form of the equation \(e^{x}=5\) is \(\boxed{\ln5=x}\). (b) The logarithmic form of the equation \(e^{4}=x\) is \(\boxed{\ln x=4}\).