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(6z)
logarithm subscript 3 baseline left parenthesis 6 z right parenthesis

log3(8z)

Answer 1

To combine the expression \( \log_3 z + \log_3 2 + \log_3 4 \) into a single logarithm, we can use the properties of logarithms.

1. The sum of logarithms can be expressed as the logarithm of the product: \[ \log_3 z + \log_3 2 + \log_3 4 = \log_3 (z \cdot 2 \cdot 4) \]

2. Calculate the product: \[ 2 \cdot 4 = 8 \]

3. Now, substitute back: \[ \log_3 (z \cdot 8) = \log_3 (8z) \]

So, the expression \( \log_3 z + \log_3 2 + \log_3 4 \) as a single logarithm is \( \log_3 (8z) \).

The correct response is:

log3(8z)