We are tasked with simplifying the expression $3 \log_b 2 - \log_b 8$ into a single logarithmic term. Here's how we do it step by step:

Step 1: Apply the power rule of logarithms

The power rule of logarithms states that $a \log_b x = \log_b (x^a)$. Using this rule, we rewrite the first term:

$3 \log_b 2 = \log_b (2^3) = \log_b 8.$

So the expression becomes:

$\log_b 8 - \log_b 8.$

Step 2: Simplify the expression

The difference of two identical logarithms is 0 because:

$\log_b 8 - \log_b 8 = 0.$

Final Answer:

$0.$

Would you like more details or further examples?

Here are 5 related questions you can explore:

1. What are the fundamental properties of logarithms?
2. How do you simplify $\log_b x^a + \log_b y^b$?
3. What happens when you add two logarithms with the same base?
4. How do you expand logarithmic expressions?
5. How can logarithms be used to solve exponential equations?

Tip: Always check if logarithmic terms can be combined or simplified using basic properties!