Discussion Forum

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

Answer:

Explanation:

$\frac{9^{n} \times 3^{5} \times \left(27\right)^{3}}{3 \times \left(81\right)^{4}}=27$ $\Leftrightarrow \frac{\left(3^{2}\right)^{n} \times 3^{5} \times \left(3^{3}\right)^{3}}{3 \times \left(3\right)^{4\times 4}}=3^{3}$ $\Leftrightarrow \frac{\left(3\right)^{2n} \times 3^{5} \times \left(3\right)^{3\times 3}}{3 \times \left(3\right)^{4\times 4}}=3^{3}$ $\Leftrightarrow\frac{3^{2n+5+9}}{3 \times 3^{16}}=3^{3}$ $\Leftrightarrow\frac{3^{2n+14}}{ 3^{17}}=3^{3}$ $\Leftrightarrow 3^{\left(2n+14-17\right)}=3^{3}$ $\Leftrightarrow 3^{\left(2n-3\right)}=3^{3}$ $2n-3 = 3 \Leftrightarrow 2n=6$ $\Leftrightarrow n=3$