If $\frac{9^n \times 3^5 \times (27)^3}{3 \times (81)^4} = 243$, then the value of n is –

Explanation

$\frac{9^n \times 3^5 \times (27)^3}{3 \times (81)^4} = 243$ $\Rightarrow \frac{(3^2)^n \times 3^5 \times (3^3)^3}{3 \times (3^4)^4} = 3^5$ $\Rightarrow \frac{3^{2n} \times 3^5 \times 3^9}{3 \times 3^{16}} = 3^5$ $3^{2n+5+9} = 3^{5+1+16}$ $3^{2n+14} = 3^{22}$ $2n + 14 = 22$ $2n = 22 - 14 = 8$ $n = \frac{8}{2} = 4$