Logarithmic Equation

Applying base changing theorem, $3^{log_{n} x}$ $+5 \times 3^{log_{n} x}=3$ , $log_{n} x \times log(3)$ $=log(1/2), log_{n} x=log_{3}(1/2)$ From second equation, for all $3^{2m}$ divided by 8, fractional part is 1/8(For proof write it as $9^{m}$ and it as $(1+8)^{m}$ . Use binomial expansion to get remainder 1 when divided by 8 and thus fractional part is 1/8) Thus $x=1/8$ . Therefore $n=27$ .
( $n \choose 2$ $-n)$ / $(2\times n)=(n-3)/4=24/4=6$