If 124+2x2=(243)3x2−2, then x =

124+2x2=(243)3x2−2⇒124+2x2=[(12)3/2]3x2−2⇒4+2x2=32(3x2−2)⇒8+4x2=9x2−6⇒5x2=14⇒x2=14/5⇒x=±14/5

If 124+2x2=(243)3x2−2, then x =

124+2x2=(243)3x2−2⇒124+2x2=[(12)3/2]3x2−2⇒4+2x2=32(3x2−2)⇒8+4x2=9x2−6⇒5x2=14⇒x2=14/5⇒x=±14/5

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

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$\pm \sqrt{13 / 12}$

$\pm \sqrt{14 / 5}$

$\pm \sqrt{12 / 13}$

$\pm \sqrt{5 / 14}$

answer is B.

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$12^{4 + 2 x^{2}} = {(24 \sqrt{3})}^{3 x^{2} - 2} \Rightarrow 12^{4 + 2 x^{2}} = {[{(12)}^{3 / 2}]}^{3 x^{2} - 2} \Rightarrow 4 + 2 x^{2} = \frac{3}{2} (3 x^{2} - 2)$

$\Rightarrow 8 + 4 x^{2} = 9 x^{2} - 6 \Rightarrow 5 x^{2} = 14 \Rightarrow x^{2} = 14 / 5 \Rightarrow x = \pm \sqrt{14 / 5}$

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