Corrigé du 42 P. 298

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a. $\ln\left(\mathrm e^{-5}\right) = -5$;

b. $\mathrm e^{\ln\dfrac 1 2} = \dfrac 1 2$;

c. $\ln\left(\mathrm e^{-1}\right) =\ln\left(\dfrac 1 {\mathrm e}\right) = -1$;

d. $\ln\left(\mathrm e^{\dfrac 1 {\mathrm e}}\right) = \dfrac 1 {\mathrm e}$;

e. $\mathrm e^{\ln(\sqrt 2)}=\sqrt 2$;

f. $\ln\left(\mathrm e^{3/7}\right) = \dfrac 3 7$.

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