Is it possible to express f(x)=(c_1a_1^x+c_2a_2^x)/(c_3a_3^x+c_4a_4^x) in the form ce^(dx) ?

orkesruim40

orkesruim40

Answered question

2022-08-11

Is it possible to express f ( x ) = C 1 a 1 x + C 2 a 2 x C 3 a 3 x + C 4 a 4 x in the form c e d x ?

Answer & Explanation

Deja Navarro

Deja Navarro

Beginner2022-08-12Added 17 answers

To express f(x) as c e d x , usually no. To approximate it, often yes. For example, for large x, look at the four exponentials, and the bigger ones win.
For example,
5 2 x 6 4 x 2 x + 3 3 x 2 ( 4 3 ) x as  x
which we do by noting 4 x defeats 2 x in the numerator, and 3 x defeats 2 x in the denominator:
5 2 x 6 4 x 2 x + 3 3 x = 5 ( 2 / 3 ) x 6 ( 4 / 3 ) x ( 2 / 3 ) x + 3 ( 3 / 3 ) x 0 6 ( 4 / 3 ) x 0 + 3 = 2 ( 4 3 ) x

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