The temperature of a fire room changes over time. For a certain fire room, let the initial temperature be $T _ { 0 } \left( {}^{\circ}\mathrm{C} \right)$ and the temperature $t$ minutes after the fire starts be $T \left( {}^{\circ}\mathrm{C} \right)$. The following equation holds. $T = T _ { 0 } + k \log ( 8t + 1 ) \quad ($ where $k$ is a constant.$)$ In this fire room with an initial temperature of $20^{\circ}\mathrm{C}$, the temperature was $365^{\circ}\mathrm{C}$ after $\frac{9}{8}$ minutes from the start of the fire, and the temperature was $710^{\circ}\mathrm{C}$ after $a$ minutes from the start of the fire. What is the value of $a$? [3 points] (1) $\frac{99}{8}$ (2) $\frac{109}{8}$ (3) $\frac{119}{8}$ (4) $\frac{129}{8}$ (5) $\frac{139}{8}$
The temperature of a fire room changes over time. For a certain fire room, let the initial temperature be $T _ { 0 } \left( {}^{\circ}\mathrm{C} \right)$ and the temperature $t$ minutes after the fire starts be $T \left( {}^{\circ}\mathrm{C} \right)$. The following equation holds.\\
$T = T _ { 0 } + k \log ( 8t + 1 ) \quad ($ where $k$ is a constant.$)$\\
In this fire room with an initial temperature of $20^{\circ}\mathrm{C}$, the temperature was $365^{\circ}\mathrm{C}$ after $\frac{9}{8}$ minutes from the start of the fire, and the temperature was $710^{\circ}\mathrm{C}$ after $a$ minutes from the start of the fire. What is the value of $a$? [3 points]\\
(1) $\frac{99}{8}$\\
(2) $\frac{109}{8}$\\
(3) $\frac{119}{8}$\\
(4) $\frac{129}{8}$\\
(5) $\frac{139}{8}$