Question 2: Write the following as a single logarithm:
\((v)\) \(\quad\) \(4\log_5\ x-\log_5\ y+\log_5\ z \)
Solution:
\[
\begin{align*}
&=4\log_{5} x-\log_{5} y+\log_{5} z\\
&=\log_{5} x^{4} -\log_{5} y+\log_{5} z\\
&=\log_{5}\frac{x^{4}}{y} +\log_{5} z\\
&=\log_{5}\frac{x^{4} z}{y}\\
\end{align*}
\]