To expand [tex]\(\log \frac{y^4}{z}\)[/tex] using the properties of logarithms, we follow these steps:
1. Apply the Quotient Rule: The quotient rule for logarithms states that [tex]\(\log \frac{a}{b} = \log a - \log b\)[/tex]. Applying this to our expression, we get:
[tex]\[
\log \frac{y^4}{z} = \log (y^4) - \log (z)
\][/tex]
2. Apply the Power Rule: The power rule for logarithms states that [tex]\(\log (a^b) = b \log (a)\)[/tex]. For the term [tex]\(\log (y^4)\)[/tex], we apply the power rule:
[tex]\[
\log (y^4) = 4 \log (y)
\][/tex]
3. Combine the Results: Substituting this back into our expression, we have:
[tex]\[
\log \frac{y^4}{z} = 4 \log (y) - \log (z)
\][/tex]
Thus, the expanded form of [tex]\(\log \frac{y^4}{z}\)[/tex] is:
[tex]\[
4 \log (y) - \log (z)
\][/tex]
