A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated ($P$) by the metal. The sensor has a scale that displays ${\log }_2\left(\frac{P}{P_0}\right)$, where $P_0$ is a constant. When the metal surface is at a temperature of $487 °\mathrm{C}$, the sensor shows a value $1$. Assume that the emissivity of the metallic surface remains constant. What is the value displayed by the sensor when the temperature of the metal surface is raised to $2767 °\mathrm{C}$?