Show that the equation $\displaystyle ln(1+e^x) = cos(x)$ has infinitely many negative solutions. Is there a positive solution? Is it unique?
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Originally Posted by DaRush19 Show that the equation $\displaystyle ln(1+e^x) = cos(x)$ has infinitely many negative solutions. Is there a positive solution? Is it unique? Have you looked at the graph of the two functions? That will tell you a lot. Note that $\displaystyle x<0$ implies $\displaystyle 0<\ln(1+e^x)<1$.
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