Ans: $x=3^{y+2}$
Since $G$ passes through $(243, 3)$, then we have
Since $G$ passes through $(243, 3)$, then we have
$\begin{array}{rcl}
3 & = & a + \log_b (243) \ \ldots\textstyle\unicode{x2460}
\end{array}$
Since the $x$-intercept of $G$ is $9$, then we have
$\begin{array}{rcl}
0 & = & a + \log_b (9) \ \ldots \textstyle\unicode{x2461}
\end{array}$
$\textstyle\unicode{x2460} – \textstyle\unicode{x2461}$, we have
$\begin{array}{rcl}
3 & = & \log_b 243 – \log_b 9 \\
3 & = & \log_b \dfrac{243}{9} \\
3 & = & \log_b 27 \\
b^3 & = & 27 \\
b & = & 3
\end{array}$
Sub. $b=3$ into $\unicode{x2461}$, we have
$\begin{array}{rcl}
0 & = & a + \log_3 9 \\
a & = & – \log_3 9 \\
a & = & -2
\end{array}$
Hence, we have
$\begin{array}{rcl}
y & = & -2 + \log_3 x \\
y + 2 & = & \log_3 x \\
x & = & 3^{y+2}
\end{array}$
