Corrigé du 44 P. 298
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a.
$\ln(x) = 4 \iff x=\mathrm e^4$.
Donc $S = \big\{\mathrm e^4\big\}$.
b.
$3\ln(x) = -5 \iff \ln(x) = -\dfrac53 \iff x = \mathrm e^{-5/3}$.
Donc $S = \big\{\mathrm e^{-5/3}\big\}$.
c.
$\ln(x) - \sqrt 3 = 0 \iff \ln(x) = \sqrt 3 \iff x = \mathrm e^{\sqrt3}$.
Donc $S = \big\{\mathrm e^{\sqrt3}\big\}$.
d.
$\ln(3x) = 1 \iff 3x = \mathrm e^1 = \mathrm e \iff x = \dfrac{\mathrm e}3$.
Donc $S = \left\{\dfrac{\mathrm e}3\right\}$.
e.
$1-2\ln(x) = 0 \iff 2\ln(x) = 1 \iff \ln(x) = \dfrac12$
$\iff x = \mathrm e^{1/2} = \sqrt{\mathrm e}$.
Donc $S = \left\{\sqrt{\mathrm e}\right\}$.
f.
$\left[\ln(x)\right]^2 = 1 \iff
\begin{cases} \ln(x) = -1\\ \text{ou} \\ \ln(x) = 1\end{cases}
\iff
\begin{cases}x = \mathrm e^{-1} = \frac1{\mathrm e}\\x = \mathrm e^1 = \mathrm e\end{cases}$.
Donc $S = \left\{\dfrac1{\mathrm e};\mathrm e\right\}$.
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