Question

rewrite as a logarithmic equation.
$e^{2}=y$

Explanation:

Step1: Recall the exponential - logarithmic conversion formula

The exponential form \(a^{x}=b\) (where \(a > 0,a
eq1\)) can be converted to the logarithmic form \(\log_{a}b=x\). For the natural exponential function, the base \(a = e\), and the natural logarithm is denoted as \(\ln\) (where \(\ln x=\log_{e}x\)).
Given the exponential equation \(e^{2}=y\), comparing with \(a^{x}=b\) (here \(a = e\), \(x = 2\), \(b = y\)).

Step2: Apply the conversion formula

Using the formula for converting exponential to logarithmic form (with base \(e\), so we use the natural logarithm), we get \(\ln y=2\) (since if \(e^{x}=y\), then \(\ln y=x\)).

Answer:

\(\ln y = 2\)