Let the unknown be x
[tex] \sqrt{3} = 27^x [/tex]
[tex] 3^\frac{1}{2} = 3^{3x} [/tex]
Both the base number are 3, so we equate the exponent:
[tex] \dfrac{1}{2} = 3x [/tex]
[tex] x = \dfrac{1}{2} \div 3 [/tex]
[tex] x = \dfrac{1}{2} \times \dfrac{1}{3} [/tex]
[tex] x = \dfrac{1}{6} [/tex]
Answer: 1/6
