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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)
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.
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.