Question

How do you solve `600/(1+e^-x)=550`?

Answer 1

`2.398` `("to 2d.p")`

Explanation:

We start off with `600/(1+e^-x)=550`

We want the `x` on its own, and it isn't useful in a denominator, so we will switch the `550` with the `1+e^(-x)` to get:
`600/550=12/11=1+e^(-x)`

We still need the numbers on one side, so we take away 1 from each side:
`e^(-x)=12/11-1=1/11`

To remove the `e` we take the `ln` of both sides:
`ln(e^(-x))=-x=ln(1/11)`

Now, we just have to divide both sides by -1 to get:
`x=-ln(1/11)=2.398` `("to 2d.p")`