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The given problem asks for the exponential equation equivalent to the logarithmic equation:

\[
\ln x = 7
\]

To find the equivalent exponential form, recall that the natural logarithm function \(\ln x\) is the logarithm with base \(e\). The logarithmic equation \(\ln x = 7\) can be rewritten in its exponential form as:

\[
x = e^7
\]

Thus, the exponential equation equivalent to \(\ln x = 7\) is:

\[
x = e^7
\]

Would you like more details or have any questions about this conversion process?

### Further Questions for Practice:

1. What is the exponential form of \(\log_{10}(x) = 2\)?
2. How do you convert an exponential equation to a logarithmic form?
3. What does \(e\) represent in mathematics?
4. How do you solve equations involving natural logarithms?
5. What is the base of a common logarithm?

**Tip:** Remember, logarithms and exponents are inverse operations. Knowing how to switch between forms can be very useful in solving equations.

Which of the following exponential equations is equivalent to the logarithmic equation ln x = 7?

Find the exponential equation equivalent to the logarithmic equation ln x = 7. Understand the relationship between logarithms and exponents, and how to convert between the two forms.

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