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.