I1.1 Find $a$ if $a=\log _{5} \frac{(125)(625)}{25}$.
I1.2 If $\left(r+\frac{1}{r}\right)^{2}=a-2$ and $r^{3}+\frac{1}{r^{3}}=b$, find $b$.
I1.3 If one root of the equation $x^{3}+c x+10=b$ is 2 , find $c$.
I1.4 Find $d$ if $9^{d+2}=(6489+c)+9^{d}$. (Reference: 1986 FG7.4)
$$
\begin{array}{l}
a=\log _{5} \frac{5^{3} \cdot 5^{4}}{5^{2}}=\log _{5} 5^{5} \\
a=5 \\
\left(r+\frac{1}{r}\right)^{2}=r^{2}+2+\frac{1}{r^{2}}=3 \Rightarrow r^{2}+\frac{1}{r^{2}}=1 \\
b=r^{3}+\frac{1}{r^{3}}=\left(r+\frac{1}{r}\right)\left(r^{2}-1+\frac{1}{r^{2}}\right)=\left(r+\frac{1}{r}\right)(1-1)=0
\end{array}
$$

Put $x=2$ into the equation: $8+2 c+10=0$
$$
\begin{array}{l}
c=-9 \\
81 \times 9^{d}=6480+9^{d} \\
80 \times 9^{d}=6480 \Rightarrow 9^{d}=81 \\
d=2
\end{array}
$$