Question

plez tell me the solution​

Answer 1

Answer:

1/2

Step-by-step explanation:

$3^x = \dfrac{9}{27^x}$

Write every term as exponents of 3:

$3^x = \dfrac{3^2}{3^{3x}}$

Cross multiply:

$(3^x)(3^{3x} )= 3^2$

Apply (aˣ)(aⁿ) = aˣ⁺ⁿ:

$3^{x + 3x} = 3^2$

$3^{4x} = 3^2$

Since both the number are 3, the exponents must be equal:

$4x = 2$

$x = \dfrac{1}{2}$

Answer: 1/2

Answer 2

Answer:

$\underline{\bold{ \frac{1}{2} }}$

Step-by-step explanation:

$3^x = \frac{9}{27^x} \\\implies 3^x = \frac{3^2}{3^{3x}} \\\implies (3^x)(3^{3x}) = 3^2\\\implies 3^{x + 3x} = 3^2\\\implies 3^{4x} = 3^2\\Since\: both\: the\: number\: are\: 3,\: the\: exponents\: must\: be\: equal:\\4x = 2 \\\implies x = \frac{2}{4} =\underline{\bold{ \frac{1}{2} }}$