To solve \(3 \log_b(2) - \log_b(4)\), we can use the properties of logarithms to simplify this expression.

### Step-by-Step Solution

1. **Expand \(3 \log_b(2)\)** using the power rule of logarithms:
   \[
   3 \log_b(2) = \log_b(2^3) = \log_b(8)
   \]

   So the expression becomes:
   \[
   \log_b(8) - \log_b(4)
   \]

2. **Apply the Quotient Rule** for logarithms, which states that \(\log_b(x) - \log_b(y) = \log_b\left(\frac{x}{y}\right)\):
   \[
   \log_b(8) - \log_b(4) = \log_b\left(\frac{8}{4}\right)
   \]

3. **Simplify the fraction** inside the logarithm:
   \[
   \frac{8}{4} = 2
   \]
   So the expression becomes:
   \[
   \log_b(2)
   \]

### Final Answer
\[
3 \log_b(2) - \log_b(4) = \log_b(2)
\]

Would you like more details, or do you have any questions?

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Here are some related questions you might find interesting:
1. How would the solution change if the expression was \(3 \log_b(2) + \log_b(4)\)?
2. What is the result of \(2 \log_b(3) - \log_b(9)\)?
3. How can you solve \(\log_b(x^3) - \log_b(x)\)?
4. How do the product, quotient, and power rules of logarithms apply to expressions involving multiple variables?
5. How do you convert logarithmic expressions to exponential form?

**Tip:** Remember that using properties of logarithms, such as the power, product, and quotient rules, can greatly simplify complex expressions.

This step-by-step guide demonstrates how to simplify the expression 3logb(2) - logb(4) by applying the power and quotient rules of logarithms. Understand how these properties help to break down and solve complex logarithmic expressions. Ideal for students in Grades 9-10 studying algebra.

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