Help!! Impossible Or Not??

[thomasrbolton]

HELP! Impossible or not? rearrange eqn to make x the subject

I am currently undertaking a masters in mathematics and am doing some statistical modelling.
I desperately need to rearrange the following equation to make x the subject (x=...)
I cannot do this, is it possibLe, if so can you show me the solution. I have been aLl around the houses with this problem, attempting to use binomial, substitions etc.
Please help! The equation can be seen below.


K = (x((1+x)^n))/(((1+x)^n)-1)

[Mridul]

Hi,

Binomial expansion of (1+x)^n is

1 + nx + {n(n-1)/2!}*x^2 + {n(n-1)(n-2)/3!}*x^3 + .....................

When n is small you can ignore the higher terms so that:

(1+x)^n becomes 1 + nx.

Given equation:

K = (x((1+x)^n))/(((1+x)^n)-1)

K = (x(1+nx))/(1+nx-1)

K = x(1+nx)/nx

Kn = 1+nx

x = (Kn-1)/n

Hope that helps.

[Mridul]

If I consider higher terms, I am stuck on

1. Putting x = cos y + i sin y .

2. Putting x = tan^2(y) .

3. Taking log on both sides and trying to rearrange.