27^x=9/3^x⇒ (3^3)^x=3^2/3^x ⇒ 3^3x× 3^x=3^2⇒ 3^3x+x=3^2 ⇒ 3^4x=3^2 Comparing,we get 4x=2⇒ x=2/4=1/2 ∴ x=1/2 ...

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Laws of Exponents for Real Numbers

If 27x=9/3x, ...

Question

If $27^{x} = \frac{9}{3^{x}}$ , find x.

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Solution

$27^{x} = \frac{9}{3^{x}} \Rightarrow (3^{3})^{x} = \frac{3^{2}}{3^{x}} \Rightarrow 3^{3 x} \times 3^{x} = 3^{2} \Rightarrow 3^{3 x + x} = 3^{2} \Rightarrow 3^{4 x} = 3^{2} C o m p a r i n g, w e g e t 4 x = 2 \Rightarrow x = \frac{2}{4} = \frac{1}{2} ∴ x = \frac{1}{2}$

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