To simplify the expression $2\log_b(3) - \log_b(9)$, we can use the properties of logarithms.

1. Apply the Power Rule: Rewrite $2\log_b(3)$ using the power rule of logarithms, $k \cdot \log_b(x) = \log_b(x^k)$: $2\log_b(3) = \log_b(3^2) = \log_b(9)$

2. Substitute and Simplify: Substitute this back into the expression: $2\log_b(3) - \log_b(9) = \log_b(9) - \log_b(9)$

3. Apply the Difference Rule: Since $\log_b(9) - \log_b(9) = 0$, the entire expression simplifies to: $0$

Thus, the simplified form is: $\boxed{0}$

Would you like further details or have any questions?

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Here are 5 related questions to deepen understanding:

1. How would the expression change if the base $b$ were a specific number, like 10?
2. Can you use logarithmic properties to simplify $\log_b(6) + \log_b(4)$?
3. How do you apply logarithmic properties to simplify $\log_b(27) - 3\log_b(3)$?
4. What is the simplified form of $3\log_b(5) - \log_b(125)$?
5. How can the logarithmic change-of-base formula help evaluate logarithmic expressions?

Tip: The properties of logarithms—product, quotient, and power—are fundamental for simplifying expressions efficiently.