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Sagot :
Answer:
x = 1.3863
Explanation:
We can rewrite our equation as
[tex](e^x)^2-e^x-12=0[/tex]which can be factored as
[tex](e^x+3)(e^x-4)=0[/tex]Therefore, the two equations we must solve are
[tex]\begin{gathered} e^x+3=0 \\ e^x-4=0 \end{gathered}[/tex]The first equation gives
[tex]\begin{gathered} e^x+3=0 \\ \Rightarrow e^x=-3 \end{gathered}[/tex]Since the natural logarithm can never give a negative number, the above equation is undefined.
Now the second equation gives
[tex]e^x-4=0[/tex][tex]e^x=4[/tex]taking the natural log of both sides gives
[tex]\ln[e^x]=\ln[4][/tex][tex]\boxed{x=\ln[4].}[/tex]which we evaluate to get (rounded to the nearest four decimal places)
[tex]\boxed{x=1.3862.}[/tex]which is our answer!
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