How can I solve
$$e^x=\frac 1{x+5}$$
I tried
$$xe^x+5e^x=1$$
$$xe^x=1-5e^x$$
$$W(xe^x)=W(1-5e^x)$$
$$W(1-5x)=x$$
But, I stucked here. I need to find the real solutions.
2026-04-02 14:06:11.1775138771
How can I solve $e^x=\frac 1{x+5}$?
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HINT
Multiply both side $e^5$, then you get
$$ \begin{align}e^{x+5}=\frac {e^5}{x+5}&\implies (x+5)e^{x+5}=e^5\\ &\implies x+5=W(e^5)\end{align} $$