Question

Rewrite log3 z + log3 2 + log3 4 as a single logarithm

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. Specifically, we can use the property that states:

\[
\log_b a + \log_b c = \log_b (ac)
\]

We can apply this property step-by-step:

1. Combine \( \log_3 z \) and \( \log_3 2 \):

\[
\log_3 z + \log_3 2 = \log_3 (z \cdot 2) = \log_3 (2z)
\]

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:

\[
\log_3 (8z)
\]