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Steps on how to solve 50=40e^0.027x

Sagot :

[tex]40{ e }^{ 0.027x }=50\\ \\ \frac { 40{ e }^{ 0.027x } }{ 40 } =\frac { 50 }{ 40 } \\ \\ \\ { e }^{ 0.027x }=\frac { 5 }{ 4 }[/tex]

[tex]\\ \\ \ln { \left( \frac { 5 }{ 4 } \right) } =0.027x\\ \\ \ln { 5 } -\ln { 4 } =\frac { 27 }{ 1000 } x[/tex]

[tex]\\ \\ \ln { 5 } -\ln { \left( { 2 }^{ 2 } \right) } =\frac { 27 }{ 1000 } x[/tex]

[tex]\\ \\ \ln { 5 } -2\ln { 2 } =\frac { 27 }{ 1000 } x\\ \\ \frac { 1000 }{ 27 } \left( \ln { 5-2\ln { 2 } } \right) =\frac { 27 }{ 1000 } x\cdot \frac { 1000 }{ 27 }[/tex]

[tex]\\ \\ x=\frac { 1000 }{ 27 } \left( \ln { 5 } -2\ln { 2 } \right) [/tex]
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