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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.

Rewrite the exponential equation e^3 = y as a logarithmic equation.

Learn how to rewrite the exponential equation e^3 = y into its logarithmic form. This problem covers essential concepts in logarithms and exponential functions, with a focus on the natural logarithm. Suitable for students in Grades 10-12.

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