Apologies for this question but I want to solve for $t$ in the following, and the answer is that we cannot solve for $t$ but I do not know why:

$904.281e^{-0.085t} = 0$. Why can we not solve for $t$ ? Why can't we take log of the products on the left and log of 0 on the right?

Thank you

  • 3
    $\begingroup$ $\log (0)$ is not defined... $\endgroup$
    – John Lou
    Nov 1, 2017 at 15:36
  • 2
    $\begingroup$ consider the graph of $f(t) = e^{-0.085t}$. It is clear that it never intercepts the t-axis. Hence there is no solution for $f(t) = 0$ $\endgroup$
    – Sul
    Nov 1, 2017 at 15:37
  • $\begingroup$ in less rigorous language, "t equals infinity". $\endgroup$
    – John Joy
    Nov 1, 2017 at 15:45

1 Answer 1


The logarithm is a function from $\Bbb{R}_{>0}$ to $\Bbb{R}$, and as such inherently not defined at zero. Thus taking $log(f(x_0))$ has no meaning when $f(x_0)=0$.


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