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

1.	If 27x \(=\frac{9}{{3}^x}\),find x.
Answer» We have, (27)^x = 9 / 3^x (3³) ^x = 3² / 3^x 3 ^3x = 3 ^{2 – x} 3x = 2 – x {On equating exponents} 3x + x = 2 4x = 2 x = \(\frac{2}{4}\) \(=\frac{1}{2}\) Hence, the value of x is \(\frac{1}{2}\)

Answer»

We have,

(27)^x = 9 / 3^x

(3³) ^x = 3² / 3^x

3 ^3x = 3 ^{2 – x}

3x = 2 – x {On equating exponents}

3x + x = 2

4x = 2

x = \(\frac{2}{4}\) \(=\frac{1}{2}\)

Hence, the value of x is \(\frac{1}{2}\)

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