Question

rewrite the expression $log_{3} z + log_{3} 2 + log_{3} 4$ as a single logarithm. (1 point)
\bigcirc $\log_{3}(8z)$
\bigcirc $\log_{3}(z + 6)$
\bigcirc $\log_{3}(6z)$
\bigcirc $\log_{3}(24z)$

Explanation:

Step1: Recall log addition rule

The logarithm addition rule states that \(\log_b M+\log_b N = \log_b(MN)\) for the same base \(b\) (where \(b>0,b
eq1,M>0,N>0\)). We can apply this rule to combine the given logarithms.

First, combine \(\log_3 2\) and \(\log_3 4\) using the addition rule: \(\log_3 2+\log_3 4=\log_3(2\times4)=\log_3 8\)

Step2: Combine with \(\log_3 z\)

Now, we have \(\log_3 z+\log_3 8\). Again, apply the logarithm addition rule: \(\log_3 z+\log_3 8=\log_3(z\times8)=\log_3(8z)\)

Answer:

\(\log_3(8z)\) (corresponding to the option: \(\boldsymbol{\log_3(8z)}\))