To rewrite the given exponential equation $e^3 = y$ as a logarithmic equation, you use the definition of a logarithm.

The exponential equation $e^3 = y$ can be rewritten in logarithmic form as:

$\log_e(y) = 3$

Or, more commonly, since the base $e$ logarithm is known as the natural logarithm:

$\ln(y) = 3$

Would you like further details or have any questions?

Here are some related questions for further exploration:

1. How would you rewrite $10^x = y$ as a logarithmic equation?
2. What is the logarithmic form of $2^5 = 32$?
3. How do you solve the equation $\ln(y) = 3$ for $y$?
4. What is the difference between natural logarithms and common logarithms?
5. How do you convert a logarithmic equation back into an exponential equation?

Tip: Remember that the natural logarithm $\ln(x)$ is just a logarithm with base $e$, which is approximately 2.718.