Rewrite the expression log3z+log32+log34

Question

as a single logarithm.(1 point)
Responses

log3(z+6)
logarithm subscript 3 baseline left parenthesis z plus 6 right parenthesis

log3(24z)
logarithm subscript 3 baseline left parenthesis 24 z right parenthesis

log3(8z)
logarithm subscript 3 baseline left parenthesis 8 z right parenthesis

log3(6z)

Answer 1

To combine the expression \( \log_3 z + \log_3 2 + \log_3 4 \) as a single logarithm, we can use the properties of logarithms. Specifically, we can use the property that states \( \log_b a + \log_b c = \log_b (a \cdot c) \).

1. Start with the original expression: \[ \log_3 z + \log_3 2 + \log_3 4 \]

2. Combine the first two logs: \[ \log_3 (z \cdot 2) + \log_3 4 = \log_3 (2z) + \log_3 4 \]

3. Now combine \( \log_3 (2z) + \log_3 4 \): \[ \log_3 (2z \cdot 4) = \log_3 (8z) \]

So, the expression \( \log_3 z + \log_3 2 + \log_3 4 \) can be rewritten as: \[ \log_3 (8z) \]

Thus, the correct response is: log3(8z)