prove that height of a binary tree with n leaves is $\displaystyle \Omega(log_{2}n)$

?

at level 0 we have 1 leaf

at level 1 we have 2 leaves

etc..

$\displaystyle 2^{0}+2^{1}+2^{2}+..+2^{x}=n$

so the sum is $\displaystyle 2^{x+1}-1=n$

$\displaystyle x=log_{2}(n+1)-1$

and $\displaystyle x\in\Omega(log_{2}n)$

and futher more $\displaystyle x\in\theta(log_{2}n)$

first question:

what formula did they use to calculate the sum

(i have here q>1)

?

second question:

i know the definition of \Omega

it means that our x is lagrer equal to C*log_{2}n

$\displaystyle \theta

$ means that x is bounded by to functions

i cant see how they got to the conclution that $\displaystyle x\in\Omega(log_{2}n)

$ and futher more $\displaystyle x\in\theta(log_{2}n)

$

?