The given equation is $81 = 9^2$, and you are asked to write it in logarithmic form.

The general rule for converting to logarithmic form:

If $a^b = c$, then in logarithmic form, this is written as: $\log_a(c) = b$

Applying this rule:

Here:

• Base $a = 9$,
• Exponent $b = 2$,
• Result $c = 81$.

The logarithmic form is: $\log_9(81) = 2$

Would you like a detailed explanation or help with any related topics?

Here are 5 related questions for further exploration:

1. How do you convert $\log_9(81) = 2$ back into its exponential form?
2. What is the logarithmic form of $27 = 3^3$?
3. How do you evaluate logarithms with different bases, such as $\log_2(8)$?
4. What is the difference between natural logarithms ($\ln$) and common logarithms ($\log$)?
5. How can you simplify expressions involving $\log(a \cdot b)$ or $\log(a / b)$?

Tip: Always ensure the base of a logarithmic expression is positive and not equal to 1.