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To convert the logarithmic equation \( \log_4 2 = \frac{1}{2} \) into exponential form, we can follow this principle:

If \( \log_b a = c \), then the exponential form is \( b^c = a \).

### Solution:
Given:
\[
\log_4 2 = \frac{1}{2}
\]

This implies:
\[
4^{\frac{1}{2}} = 2
\]

So, the exponential form of the equation \( \log_4 2 = \frac{1}{2} \) is:
\[
4^{\frac{1}{2}} = 2
\]

Would you like more details on logarithmic to exponential conversions or have any further questions?

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Here are some related questions for further exploration:

1. What is the exponential form of \( \log_3 9 = 2 \)?
2. How do you convert an equation like \( \log_{10} 1000 = 3 \) into exponential form?
3. Can logarithmic equations with fractional exponents always be simplified in exponential form?
4. What is the exponential form of \( \log_2 \frac{1}{4} = -2 \)?
5. How does the base of the logarithm affect the exponential form?

**Tip:** To convert a logarithmic equation to exponential form, remember that \( \log_b a = c \) translates to \( b^c = a \).

Write the logarithmic equation \( \log_4 2 = \frac{1}{2} \) in exponential form.

Learn how to convert the logarithmic equation \( \log_4 2 = \frac{1}{2} \) to its exponential form, \( 4^{\frac{1}{2}} = 2 \). This guide explains the step-by-step process and key concepts involved in logarithmic and exponential conversions. Suitable for high school students.

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