Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 470: 89

$t=-\dfrac{\log \dfrac{T-T_0}{T_1-T_0}}{k}$

The given expression can be written as: $T-T_0=(T_1-T_0)10^{-kt}$ or,$10^{-kt}=\dfrac{T-T_0}{T_1-T_0}$ or,$-kt =\log \dfrac{T-T_0}{T_1-T_0}$ Now, we will solve for $t$. Therefore, our answer is: $t=-\dfrac{\log \dfrac{T-T_0}{T_1-T_0}}{k}$