I1.1 解方程 $\log _{5} a+\log _{3} a=\log _{5} a \cdot \log _{3} a$, 其中 $a>1$ 為實數。
Solve the equation $\log _{5} a+\log _{3} a=\log _{5} a \cdot \log _{3} a$ for real number $a>1$.
$$
\frac{\log a}{\log 5}+\frac{\log a}{\log 3}=\frac{\log a}{\log 5} \cdot \frac{\log a}{\log 3}
$$

Multiple both sides by $\log 3 \cdot \log 5$ and divide both sides by $\log a(\neq 0)$. $\log 3+\log 5=\log a$
$$
a=15
$$