Question

expand the following logarithmic expression into a sum or difference of logs. there should be no multiplication, division, or exponents in your final answer.\\(\log_{3}(x^{9})\\)\\(\bigcirc\\ 9 + \log_{3}(x)\\)\\(\bigcirc\\ 9\log_{3}(x)\\)\\(\bigcirc\\ 9 - \log_{3}(x)\\)\\(\bigcirc\\ \frac{9}{\log_{3}(x)}\\)\\(\bigcirc\\ none of the above\\)

Explanation:

Step1: Recall Log Power Rule

The power rule for logarithms states that $\log_b(a^n) = n\log_b(a)$, where $b>0, b
eq1$, $a>0$, and $n$ is a real number.

Step2: Apply the Rule to Given Expression

For the expression $\log_3(x^9)$, we identify $b = 3$, $a = x$, and $n = 9$. Applying the power rule, we get $9\log_3(x)$.

Answer:

B. $9\log_3(x)$