Let's solve the two parts of the problem:

A) Convert the statement $9^2 = 81$ to logarithmic form:

The general form to convert exponential statements to logarithmic form is: $a^b = c \quad \text{becomes} \quad \log_a(c) = b$

In this case: $9^2 = 81 \quad \text{becomes} \quad \log_9(81) = 2$

Answer for A: $\log_9(81) = 2$

B) Convert the statement $\log_9(81) = 2$ to exponential form:

The general form to convert logarithmic statements to exponential form is: $\log_a(c) = b \quad \text{becomes} \quad a^b = c$

In this case: $\log_9(81) = 2 \quad \text{becomes} \quad 9^2 = 81$

Answer for B: $9^2 = 81$

Would you like additional details or examples to reinforce the concept?

Related Questions:

1. What is the general form of logarithmic and exponential equations?
2. How do you calculate logarithms for non-perfect powers (e.g., $\log_3(10)$)?
3. What are the properties of logarithms (e.g., product, quotient, and power rules)?
4. How does changing the base of a logarithm affect the equation?
5. Can you provide a real-world application of logarithmic functions?

Tip:

When converting between logarithmic and exponential forms, always identify the base, exponent, and result clearly—it ensures accurate transformations.