[tex]\begin{gathered} \text{Given:} \\ I_0=10^{-16}\text{ }W\/cm^2 \\ I=65000\times10^{-16}\text{ }W\/cm^2\text{ (from the phrase 65,000 times }I_0) \\ L=10\log \mleft(\frac{I}{I_0}\mright)\text{ the formula for loudness} \end{gathered}[/tex]
Substitute the following values to the given formula for loudness and we get
[tex]\begin{gathered} L=10\log (\frac{I}{I_0}) \\ L=10\log (\frac{65000\times10^{-16}\text{ }W\/cm^2}{10^{-16}\text{ }W\/cm^2}) \\ L=10\log (65000) \\ L=48.12913357dB \\ L=48dB\text{ (rounded off to nearest whole number)} \end{gathered}[/tex]
Therefore, the decibel reading is approximately 48 dB.
