Question 1

If 9^2x = 27/3^x+2, then find the value of x
(a) 1/6
(b) 1)5
(c) -2/3
(d) 1/8

Question 2

Answer:

$\textsf{Option (b) 1/5 is your correct answer.}\\$

Explanation:

$\bf➤ \underline{Given-} \\$

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

$\bf ➤\underline{To\: find-} \\$

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

$\bf➤ \underline{Solution-} \\$

$\textsf{Given expression,}\\$

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

$\sf{ \implies \: {9}^(2x) * {3}^(x + 2) = 27} \\$

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

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

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

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

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

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

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

$\sf{ \implies \: x = (1)/(5) } \\$

$\bf ➤\underline{Answer-} \\$

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

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