Question

expand the logarithm. assume all expressions exist and are well - defined. write your answer as a sum or difference of base - 7 logarithms or multiples of base - 7 logarithms. the inside of each logarithm must be a distinct constant or variable. \\(\log_{7} xwv\\)

Explanation:

Step1: Recall logarithm product rule

The product rule for logarithms states that $\log_b(ac) = \log_b a + \log_b c$ for any positive numbers $a$, $c$ and base $b>0$, $b
eq1$. Here, we have $\log_7(xwv)$, which is $\log_7(x\cdot w\cdot v)$.

Step2: Apply product rule repeatedly

First, apply the product rule to $x$ and $wv$: $\log_7(x\cdot w\cdot v)=\log_7 x+\log_7(wv)$. Then, apply the product rule to $w$ and $v$ in $\log_7(wv)$: $\log_7(wv)=\log_7 w+\log_7 v$. Combining these, we get $\log_7 x+\log_7 w+\log_7 v$.

Answer:

$\log_{7}x + \log_{7}w + \log_{7}v$