Solving for x in an exponential equation Say we the following equation F(x) = (exp(a+bx))/(1 + exp(a+bx)) Now we set x=0 and we want to solve for a as a function of F_0.

Belinda Colon

Belinda Colon

Answered question

2022-11-24

Solving for x in an exponential equation
Say we the following equation
F ( x ) = exp ( a + b x ) 1 + exp ( a + b x )
Now we set x = 0 and we want to solve for a as a function of F 0 .
So that, we have:
F 0 = exp ( a ) 1 + exp ( a )
Can someone please walk me though the logarithmic transformation on how we achieve this end result
a = ln ( F 0 1 F 0 )

Answer & Explanation

Hudson Fry

Hudson Fry

Beginner2022-11-25Added 11 answers

F 0 = e a 1 + e a
F 0 + e a F 0 = e a
F 0 = e a e a F 0
F 0 = ( 1 F 0 ) e a
e a = F 0 1 F 0
a = ln ( F 0 1 F 0 )
Simon Hanna

Simon Hanna

Beginner2022-11-26Added 1 answers

F 0 = exp ( a ) 1 + exp ( a )
This leads to:
( 1 + exp ( a ) ) F 0 = exp ( a )
Thus:
F 0 = exp ( a ) ( 1 F 0 )
Dividing by 1 F 0 and taking the log, you get the result.

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