Solve for $S (t)$ in the equation
$$-c \, t = \log S(t)$$
where $t$ is time and $c$ is a constant.
$$-ct=\log S(t)$$ take $e$ for both sides $$e^{-ct}=S(t)$$
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$$-ct=\log S(t)$$ take $e$ for both sides $$e^{-ct}=S(t)$$