On the set of all non-zero reals, an operation * is defined as a^ * b= 3 a b 2 . In this group, a solution of (2^ * x ) * 3⁻¹=4⁻¹ is

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Given binary operation is a^ * b= 3 a b 2 Now, 2 * x= 3 2 2 x=3 x[ from Eq. (i) ] (ii) and (3 x)^ * 1 3 = 3 2 3 x 1 3 = 3 x 2 Then, (2^ * x )^ * 3⁻¹=4⁻¹ aligned &(3 x)^ * n 1 3 = 1 4 & [from Eq. (ii)] & 3 x 2 &= 1 4 & [from Eq. (iii)] & x &= 1 6 & aligned

On the set of all non-zero reals, an operation * is defined as a^ * b= 3 a b 2 . In this group, a solution of (2^ * x ) * 3⁻¹=4⁻¹ is

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