Question

You are asked to rewrite the expression log2 z + log2 12 - log2 5 as a single logarithm. Type your answer in the box below.

Answer 1

To rewrite the expression \( \log_2 z + \log_2 12 - \log_2 5 \) as a single logarithm, we can use the properties of logarithms:

1. **Product Property**: \( \log_b a + \log_b c = \log_b (a \cdot c) \)
2. **Quotient Property**: \( \log_b a - \log_b c = \log_b \left( \frac{a}{c} \right) \)

Applying these properties step by step:

1. Combine the first two terms:
\[
\log_2 z + \log_2 12 = \log_2 (z \cdot 12)
\]

2. Now apply the quotient property with the result from step 1:
\[
\log_2 (z \cdot 12) - \log_2 5 = \log_2 \left( \frac{z \cdot 12}{5} \right)
\]

Thus, the expression \( \log_2 z + \log_2 12 - \log_2 5 \) can be simplified to:
\[
\log_2 \left( \frac{12z}{5} \right)
\]

This is the final answer.