Question

if 9 to the power 2x = 27/3 to the power x + 2 find value of x

Answer 1

Answer:

     You will find the answer in the attachment . Hope it is helpful. Take care

Answer 2

Step-by-step explanation:

$\bf \underline{Given-}$

$\sf{ {9}^{2x} = \frac{27}{ {3}^{x + 2} } }$

$\bf \underline{To\: find-}$

$\textsf{the value of x = ?}$

$\bf \underline{Solution-}$

$\textsf{Given expression,}$

$\sf{ {9}^{2x} = \frac{27}{ {3}^{x + 2} } }$

$\sf{ \implies \: {9}^{2x} \times {3}^{x + 2} = 27}$

$\sf{ \implies \:( {3}^{2} {)}^{2x} \times {3}^{x + 2} = {3}^{3} }$

$\sf{ \implies \: {3}^{4x} \times {3}^{x + 2} = {3}^{3} }$

$\sf{ \implies \: {3}^{4x + x + 2} = {3}^{3} }$

$\sf{ \implies \: { \cancel3}^{5x + 2} = { \cancel3}^{3} }$

$\sf{ \implies \: }5x + 2 = 3$

$\sf{ \implies \: 5x = 3 - 2}$

$\sf{ \implies \: 5x = 1}$

$\sf{ \implies \: x = \frac{1}{5} }$

$\bf \underline{Hence, the\: value\: of \:x \: is \: \frac{1}{5}.}$