6.6 Exercise 120

Newton’s Law of Cooling states that the temperature $T$ of an object at any time t can be described by the equation $T = T_{s} + \left(T_{0} - T_{s}\right) e^{- k t} ,$ where $T_{s}$ is the temperature of the surrounding environment, $T_{0}$ is the initial temperature of the object, and $k$ is the cooling rate. Use the definition of a logarithm along with properties of logarithms to solve the formula for time $t$ such that $t$ is equal to a single logarithm.