# If (9^(x-2) * 3^(2x-2))/(27^(x+3)) =81, x=?

Aug 11, 2018

$x = 19$

#### Explanation:

Given

9^(x-2) × 3^(2x-2)/(27^(x+3))=81

Now,we can write, ${9}^{x - 2} = {3}^{2 \left(x - 2\right)} = {3}^{2 x - 4}$

Also, ${27}^{x + 3} = {3}^{3 \left(x + 3\right)} = {3}^{3 x + 9}$

Now using the above modifications, we can write the entire equation as,

3^(2x-4)×3^(2x-2)/3^(3x+9)=81

Or, ${3}^{2 x - 4 + 2 x - 2 - 3 x - 9} = {3}^{4}$

Or, ${3}^{x - 15} = {3}^{4}$

So, comparing we can write,

$x - 15 = 4$

Or, $x = 19$

Aug 11, 2018

$x = 19$

#### Explanation:

${9}^{x - 2} \cdot {3}^{2 x - 2} \div {27}^{x + 3} = 81$

$\therefore {\left({3}^{2}\right)}^{x - 2} \cdot {3}^{2 x - 2} \div {\left({3}^{3}\right)}^{x + 3} = {3}^{4}$

$\therefore {3}^{2 x - 4} \cdot {3}^{2 x - 2} \div {3}^{3 \left(x + 3\right)} = {3}^{4}$

$\therefore \frac{{3}^{4 x - 6}}{{3}^{3 x + 9}} = {3}^{4}$

$\therefore {3}^{4 x - 6 - 3 x - 9} = {3}^{4}$

$\therefore {3}^{x - 15} = {3}^{4}$

$\therefore x - 15 = 4$

$\therefore x = 15 + 4$

$\therefore x = 19$