Question

How do you solve `\frac { 2^ { x } } { 1- 2^ { x } } = 3`?

Answer 1

`x=-0.415`

Explanation:

Let `2^x=t`

then our equation becomes `t/(1-t)=3`

or `t=3-3t` i.e. `4t=3`

and `t=3/4`

Hence `2^x=3/4`

or `xlog2=log0.75=-0.124939`

or `x=log0.75/log2=-0.124939/0.30103`

i.e. `x=-0.415`