G1.4 Suppose $\log _{x} t=6, \log _{y} t=10$ and $\log _{z} t=15$. If $\log _{x y z} t=d$, find the value of $d$.
$\begin{array}{l}\frac{\log t}{\log x}=6, \frac{\log t}{\log y}=10, \frac{\log t}{\log z}=15 \\ \Rightarrow \frac{\log x}{\log t}=\frac{1}{6}, \frac{\log y}{\log t}=\frac{1}{10}, \frac{\log z}{\log t}=\frac{1}{15} \\ \frac{\log x}{\log t}+\frac{\log y}{\log t}+\frac{\log z}{\log t}=\frac{1}{6}+\frac{1}{10}+\frac{1}{15}=\frac{10}{30}=\frac{1}{3} \\ \frac{\log x+\log y+\log z}{\log t}=\frac{1}{3} \\ \frac{\log x y z}{\log t}=\frac{1}{3} \\ d=\frac{\log t}{\log x y z}=3\end{array}$