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$\ln 10\;;$
Corrigé
$\ln 10 = \ln(2\times 5) = \ln 2 + \ln 5$
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$\ln 100\;;$
Corrigé
$\ln 100 = \ln 10^2 = 2\ln 10 = 2\ln 2 + 2\ln 5$
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$\ln 0,0001\;;$
Corrigé
$\ln 0,000\:1=\ln\dfrac 1 {10^4} = -4\ln 10 = -4\ln 2 - 4\ln 5$
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$\ln\sqrt{1000}\;;$
Corrigé
$\ln\sqrt{1000}=\dfrac 1 2 \ln 10^3 = \dfrac 3 2 \ln 10 = \dfrac 3 2\ln 2 + \dfrac 3 2 \ln 5$
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$\ln\left(\dfrac 8 {25}\right)\;;$
Corrigé
$\ln\dfrac 8{25}=\ln 8 -\ln 25 = \ln 2^3 - \ln 5^2 = 3\ln 2 - 2\ln 5$
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$\ln\left(8\times 10^5\right)\;;$
Corrigé
$\ln(8\times 10^5) = \ln 8 + \ln 10^5 = \ln 2^3 +5\ln 10$
$=3\ln 2 + 5\ln 2 + 5\ln 5
=8\ln 2 + 5\ln 5$
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$\ln\left(32\times 10^{-8}\right)\;;$
Corrigé
$\ln(32\times 10^{-8}) = \ln 32 -8\ln 10 = \ln 2^5 - 8\ln 2 - 8\ln 5$
$=5\ln 2 -8\ln 2 -8\ln 5
=-3\ln 2 - 8\ln 5$
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$\ln(0,000\:004).$
Corrigé
$\ln(0,000\:004)=\ln \dfrac 4 {10^6}=\ln 4 -6\ln 10$
$= 2\ln 2 -6\ln 2 - 6\ln 5
=-4\ln 2 -6\ln 5$