Question

Which of the following options correctly rewrites log4 (x/5)
using the Quotient Rule of Logarithms?

Option #1: log4 x+log4 5


Option #2: log4 x−log4 5


Option #3: log4 x/log4 5


(1 point)

Answer 1

The Quotient Rule of Logarithms states that:

\[
\log_b \left( \frac{a}{c} \right) = \log_b a - \log_b c
\]

Using this rule, we can rewrite \(\log_4 \left(\frac{x}{5}\right)\) as follows:

\[
\log_4 \left(\frac{x}{5}\right) = \log_4 x - \log_4 5
\]

Thus, the correct option for rewriting \(\log_4 \left(\frac{x}{5}\right)\) using the Quotient Rule of Logarithms is:

**Option #2: \(\log_4 x - \log_4 5\)**.