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Sagot :
[tex]500{ e }^{ -0.12x }=123\\ \\ { e }^{ -\frac { 12 }{ 100 } x }=\frac { 123 }{ 500 } \\ \\ { e }^{ -\frac { 3 }{ 25 } x }=\frac { 123 }{ 500 }[/tex]
[tex]\\ \\ { \left( { e }^{ x } \right) }^{ -\frac { 3 }{ 25 } }=\frac { 123 }{ 500 } \\ \\ { e }^{ x }={ \left( \frac { 123 }{ 500 } \right) }^{ \frac { 1 }{ -\frac { 3 }{ 25 } } }[/tex]
[tex]\\ \\ { e }^{ x }={ \left( \frac { 123 }{ 500 } \right) }^{ -\frac { 25 }{ 3 } }\\ \\ \ln { \left( { \left( \frac { 123 }{ 500 } \right) }^{ -\frac { 25 }{ 3 } } \right) } =x[/tex]
[tex]\\ \\ x=-\frac { 25 }{ 3 } \ln { \left( \frac { 123 }{ 500 } \right) } [/tex]
[tex]\therefore \quad x\approx 11.7[/tex]
[tex]\\ \\ { \left( { e }^{ x } \right) }^{ -\frac { 3 }{ 25 } }=\frac { 123 }{ 500 } \\ \\ { e }^{ x }={ \left( \frac { 123 }{ 500 } \right) }^{ \frac { 1 }{ -\frac { 3 }{ 25 } } }[/tex]
[tex]\\ \\ { e }^{ x }={ \left( \frac { 123 }{ 500 } \right) }^{ -\frac { 25 }{ 3 } }\\ \\ \ln { \left( { \left( \frac { 123 }{ 500 } \right) }^{ -\frac { 25 }{ 3 } } \right) } =x[/tex]
[tex]\\ \\ x=-\frac { 25 }{ 3 } \ln { \left( \frac { 123 }{ 500 } \right) } [/tex]
[tex]\therefore \quad x\approx 11.7[/tex]
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