## Functions Modeling Change: A Preparation for Calculus, 5th Edition

First, divide both sides of the equation by $Q_o$ to get $$e^{kt}=\frac{Q}{Q_o}$$ Next, take the $\ln$ of both sides to get $$\ln e^{kt}=\ln(Q/Q_o)$$ Since $\ln a^b=b \ln a$ for all positive values of $a$, $$kt \ln e = kt = ln(Q/Q_o)$$ Finally, divide both sides by $k$ to get $$t = \frac{\ln(Q/Q_o)}{k}$$ Thus, the statement is true.