91Ó°ÊÓ

Solve, correct to 4 significant figures: \(\ln (x-2)^{2}=\ln (x-2)-\ln (x+3)+1.6\)

In an experiment involving Newton's law of cooling, the temperature \(\theta\left({ }^{\circ} \mathrm{C}\right)\) is given by \(\theta=\theta_{0} \mathrm{e}^{-k t} .\) Find the value of constant \(k\) when \(\theta_{0}=56.6^{\circ} \mathrm{C}, \theta=16.5^{\circ} \mathrm{C}\) and \(t=83.0\) seconds.