I4.1 Find $x$ if $x=\frac{\log a^{3}}{\log a^{2}}$ where $a>0$ and $a \neq 1$.
I4.2 If $y-1=\log x+\log 2-\log 3$, find $y$.
I4.3 What is $Z$ if $\log _{2} Z^{y}=3$ ?
I4.4 Find $\log _{z} y$.
$\begin{array}{l}x=\frac{\log a^{3}}{\log a^{2}}=\frac{3 \log a}{2 \log a}=\frac{3}{2} \\ y-1=\log \frac{3}{2}+\log 2-\log 3 \\ y=\log \left(\frac{3}{2} \times \frac{2}{3}\right)+1=\log 1+1=1 \\ \log _{2} Z=3 \Rightarrow Z=2^{3}=8 \\ \log _{8} 1=0\end{array}$