Here is the solution for Example 13:

Part (a): $\log_2 5 + \log_2 1.6$

Using the logarithmic property: $\log_b A + \log_b B = \log_b (A \cdot B)$ we combine the two terms: $\log_2 5 + \log_2 1.6 = \log_2 (5 \cdot 1.6).$

Simplify the product: $5 \cdot 1.6 = 8.$

Thus: $\log_2 (5 \cdot 1.6) = \log_2 8.$

Since $8 = 2^3$, we know: $\log_2 8 = 3.$

Final Answer for (a): $3$.

Part (b): $\log_6 24 + \log_6 15 - \log_6 60$

Using the logarithmic properties:

1. Addition of logs: $\log_b A + \log_b B = \log_b (A \cdot B)$,
2. Subtraction of logs: $\log_b A - \log_b C = \log_b \left( \frac{A}{C} \right).$

First, combine the terms: $\log_6 24 + \log_6 15 - \log_6 60 = \log_6 \left( \frac{24 \cdot 15}{60} \right).$

Simplify the expression inside the log: $\frac{24 \cdot 15}{60} = \frac{360}{60} = 6.$

Thus: $\log_6 \left( \frac{24 \cdot 15}{60} \right) = \log_6 6.$

Since $\log_6 6 = 1$ (because $6 = 6^1$), we get: $\log_6 6 = 1.$

Final Answer for (b): $1$.

Final Results:

• (a): $3$
• (b): $1$

Do you want a detailed explanation of any specific step? Let me know!

Related Questions:

1. Solve $\log_3 9 + \log_3 27$.
2. Simplify $\log_5 25 + \log_5 1$.
3. Evaluate $\log_4 16 - \log_4 4$.
4. Simplify $\log_7 14 + \log_7 49 - \log_7 7$.
5. Solve $\log_2 4 + \log_2 8 - \log_2 2$.

Tip: Remember, logarithmic rules make it easier to combine, split, or simplify expressions!