Question

If 9^x × 3^2 × (3^-x/2)^-2 = 1/27, Find x

Answer 1

Answer:

x = -5/3

Step-by-step explanation:

${9}^{x} \times {3}^{2} \: \times \: (\frac{1}{ \sqrt{ {3}^{x} } } ) \: = \: \frac{1}{ {3}^{3} }$

3^2x × 3^2 × 3^x = 1/3^3

3^3x + 2 = 3^3

therefore comparing both exponents..

3x + 2 = -3

3x = -5

x = -5/3

Answer 2

⋆ ⫷❥Q᭄u Σ§TiOn⫸⋆

If $\tt {9}^{x} \times {3}^{2} ( {3} ^ { \frac{- x}{2} } )^{ - 2} = \dfrac{1}{27}$ , find x .

꧁ANSWER꧂

$\tt {9}^{x} \times {3}^{2} ( {3} ^ { \frac{- x}{2} } )^{ - 2} = \dfrac{1}{27}$

$→ \tt {3}^{2x} \times {3}^{2} \times ( {3}^{x}) = {3}^{ - 3}$

$→ \tt {3}^{3x + 2} = \times {3}^{ - 3}$

As , the base are same on both sides we can equate exponent .........✍️

→ 3x + 2 = -3

→ 3x = - 3 - 2

→ 3x = -5

→ x = - 5/3