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The value of (x>1),for which the sixth term in the expansion of

{ 2

^{log2√}^{ (9^(x-1)+7) }+ 1/2^{(1/5)log2}^{(3^(x-1) +1) }}^{7 }is 84 is equal toX

^{2001}+[1/2-X]^{2001}=0 is ???1: 2000

2: 2001

3: 1000

4: 500

Above is question and its solution. I didn't get the first step itself. Explain in detail

^{n}<n^{2}, is true for all natural numbers, n>=5.^{2}+bx+c=0 is equal to n^{th}power of other than b is^{2}+2^{3}+...+2^{n}=2^{n-1}-1,is true for all natural numbers n.