rewrite the expression $log_{3} z + log_{3} 2 + log_{3} 4$ as a single logarithm. (1 point)\n\\bigcirc…
rewrite the expression $log_{3} z + log_{3} 2 + log_{3} 4$ as a single logarithm. (1 point)\n\\bigcirc $\\log_{3}(8z)$\n\\bigcirc $\\log_{3}(z + 6)$\n\\bigcirc $\\log_{3}(6z)$\n\\bigcirc $\\log_{3}(24z)$
Answer
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\neq1,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))