Question

Rewrite the expression log3z + log32+log34
as a single logarithm(1 point)
Responses

log3(z + 6)
log3(z + 6)

log3(24z)
log sub 3 of 24 z

log3(6z)
log sub 3 of 6 z

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 property of logarithms that states \( \log_b a + \log_b c = \log_b (a \cdot c) \).

1. Combine \( \log_3 z \) and \( \log_3 2 \):
\[
\log_3 z + \log_3 2 = \log_3 (2z)
\]

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

Thus, the expression \( \log_3 z + \log_3 2 + \log_3 4 \) can be rewritten as a single logarithm:

\[
\log_3 (8z)
\]

So the correct response is:
**log3(8z)**