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?

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.