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The equation presented is \( 81^{\frac{1}{2}} = 9 \). We are asked to write it in logarithmic form.

The general form for converting an exponential equation \( a^b = c \) into logarithmic form is:
\[
\log_a(c) = b
\]
where:
- \( a \) is the base,
- \( b \) is the exponent,
- \( c \) is the result.

In this case:
- \( a = 81 \),
- \( b = \frac{1}{2} \),
- \( c = 9 \).

Thus, the logarithmic form of \( 81^{\frac{1}{2}} = 9 \) is:
\[
\log_{81}(9) = \frac{1}{2}
\]

Would you like further explanation, or do you have any questions?

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Here are 5 related questions to deepen understanding:
1. How do you convert any exponential equation to logarithmic form?
2. What are the properties of logarithms that help simplify expressions?
3. How can you verify if \( \log_{81}(9) = \frac{1}{2} \) is correct?
4. What are the different bases commonly used in logarithms, and how do they affect the calculation?
5. How does the square root relate to logarithms?

**Tip:** The logarithmic form expresses the exponent as the solution, making it easier to solve for unknown exponents.

Write the equation in logarithmic form. 81^(1/2) = 9

Learn how to convert the exponential equation 81^(1/2) = 9 into logarithmic form. This problem covers key algebraic concepts such as exponent-logarithm conversion and is suitable for students in Grades 9-11.

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