Units of rate constant for the first order reaction

The integrated rate law is

Because $\log_{10}\dfrac{\mathrm{[A]_0}}{\mathrm{[A]_t}}$ is a unitless quantity, the dimensions of $k$ will be $(\text{time})^{-1}$. The units of $k$ will be $\mathrm{s^{-1}}$, $\mathrm{min^{-1}}$ or $(\text{hour})^{-1}$. …