Question

${2}^{x^{2} } = { {3}^{y} }^{2} = { {12}^{z} }^{2}$
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Answer 1

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$\underline{\large\mathcal\red{solution}}$

$2x {}^{2} = 3y {}^{2} = 12z {}^{2} = k(let) \\ 2x { }^{2} = k = > 2 = \frac{k}{x {}^{2} } \\ \\ 3y {}^{2} = k = > 3 = \frac{k}{y {}^{2} } \\ \\ 12z {}^{2} = k = > 12 = \frac{k}{z {}^{2} } \\ \\ .....now .....\\ \\ 12 = 3 \times 2 \times 2 \\ = > \frac{k}{z {}^{2} } = \frac{k}{y {}^{2} } \times \frac{k}{x {}^{2} } \times \frac{k}{x {}^{2} } \\ = > z {}^{2} = y {}^{2} x {}^{4} \\ = > z= x {}^{2} y$

$\large\mathcal\red{hope\: this \: helps \:you......}$