= Solution
For weak <damping>, the <ringdown comparison bound for two resonator modes> gives $I(t)=I(0)e^{-\omega t/Q}$. Interpreting the stated loudness comparison as an <intensity> comparison,
$$
\frac{I_L(2)}{I_H(2)}=2\exp\!\left[-2\left(\frac{2\pi(700)}{Q_L}-\frac{2\pi(6000)}{10^5}\right)\right]<1.
$$
Therefore \b[the information gives an upper bound], not a unique value:
$$
\boxed{Q_L<\frac{2\pi(700)}{2\pi(6000)/10^5+\ln2/2}\simeq6.08\times10^3.}
$$
Equality would describe equal <intensities> at two seconds; the stated strict inequality allows every smaller positive $Q_L$ consistent with the weak-damping model.
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