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Answer:
x = 2.1972
Step-by-step explanation:
[tex] {e}^{2x} - 2 {e}^{x} - 63 = 0[/tex]
Let
[tex] {e}^{x} \: be \: y[/tex]
[tex] {e}^{x(2)} - 2 {e}^{x} - 63 = 0[/tex]
y² - 2y - 63 = 0
Using Factorization method
y² - 9y + 7y - 63 = 0
y(y - 9) + 7(y - 9) = 0
(y - 9)(y + 7) = 0
y - 9 = 0 , y + 7 = 0
y = 9 , y = - 7
Therefore,
[tex] {e}^{x} = 9 \: and \: {e}^{x} = - 7[/tex]
Take In of both sides
[tex]In( {e}^{x} ) = In9[/tex]
x Ine = In 9 Applying logarithm law of same base.
x = In 9
and
[tex]In {e}^{x} \: = In( - 7)[/tex]
x Ine = In(-7) Applying logarithm law of same base
x = In (-7) is undefined.
Hence,
x = In9
x = 2.1972