If 12^{4+2x^2} = (24sqrt{3})^{3x^2-2},then x | vedclass

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(B) Given equation: $12^{4+2x^2} = (24\sqrt{3})^{3x^2-2}$ Express $24\sqrt{3}$ in terms of base $12$: $24\sqrt{3} = 12 	imes 2 	imes \sqrt{3} = 12 \

Vedclass · Accepted Answer

$\pm \sqrt{\frac{14}{5}}$

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(B) Given equation: $12^{4+2x^2} = (24\sqrt{3})^{3x^2-2}$ Express $24\sqrt{3}$ in terms of base $12$: $24\sqrt{3} = 12 	imes 2 	imes \sqrt{3} = 12 	imes \sqrt{4} 	imes \sqrt{3} = 12 	imes \sqrt{12} = 12^1 	imes 12^{1/2} = 12^{3/2}$ Substituting this into the equation: $12^{4+2x^2} = (12^{3/2})^{3x^2-2}$ $12^{4+2x^2} = 12^{\frac{3}{2}(3x^2-2)}$ Equating the exponents: $4+2x^2 = \frac{3}{2}(3x^2-2)$ $8+4x^2 = 9x^2-6$ $9x^2-4x^2 = 8+6$ $5x^2 = 14$ $x^2 = \frac{14}{5}$ $x = \pm \sqrt{\frac{14}{5}}$

If $12^{4+2x^2} = (24\sqrt{3})^{3x^2-2}$,then $x$ is equal to

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