(a)[2]
Show that $\ln(1 + e^{-x}) + 2x = 0$ may be rewritten as a quadratic equation in $e^{x}$.
(b)[4]
Hence solve $\ln(1 + e^{-x}) + 2x = 0$, and give your answer correct to 3 decimal places.
Mathematics 9709 · AS & A Level · Logarithmic and exponential functions
Logarithmic and exponential functions — practice question
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correctly remove the logarithms and state $1+e^{-x}=e^{-2x}$, or an equivalent form” …
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