A particular temperature scale is obtained according to the relation:
$$t=a e^{\alpha}+b$$
where $a$ and $b$ are constants, and $t$ is in ${ }^{\circ} \mathrm{C}$.
The thermometric property as measured by the thermometer is $\alpha$. The values of $\alpha$ at ice point and steam point are $6$ and $9$, respectively. The temperature (in ${ }^{\circ} \mathrm{C}$ ) which gives $\alpha=7$ is $\_\_\_\_\_\_\_$ (rounded off to two decimal places).
