Corrigé du 74 P. 301

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1. None of the answers is correct! \begin{flalign*} &\ln(x+1) + \ln(5) = 1& \\ \iff &\ln\left(5(x+1)\right) = 1& \\ \iff &5(x+1) = \mathrm e& \\ \iff &x + 1 = \frac{\mathrm e} 5& \\ \iff &x = \frac{\mathrm e} 5 - 1.& \end{flalign*} Therefore the correct answer is $\frac{\mathrm e}5 - 1$.

2. The correct answer is d. \[ f(1) = 2 - \mathrm e^{2\times 1 - \ln(3)} =2 - \frac{\mathrm e^{2}}{\mathrm e^{\ln(3)}} =2 - \frac{\mathrm e^2} 3 =\frac{6 - \mathrm e^2}3. \]

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