Question: 5 — Properties of logarithms
LEARNING OBJECTIVE: Convert a logarithmic expression using the properties
of logs.
The sum log₅(3)+log₅(8) can also be expressed as ____________.
a.) log₃(40)
b.) log₈(15)
c.) log₅(24)
d.) log₅(11)
1. **State the problem:** We want to simplify the expression $$\log_5(3) + \log_5(8)$$ using properties of logarithms.
2. **Recall the property:** The sum of logarithms with the same base can be combined using the product rule:
$$\log_b(x) + \log_b(y) = \log_b(x \times y)$$
3. **Apply the property:** Since both logs have base 5, we combine:
$$\log_5(3) + \log_5(8) = \log_5(3 \times 8)$$
4. **Calculate the product:**
$$3 \times 8 = 24$$
5. **Final expression:**
$$\log_5(24)$$
6. **Match with choices:** The correct answer is c.) $$\log_5(24)$$.