Question

Solve ${\log }_{3\sqrt{2}}5832$

Answer 1

$3|5832$

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$3|1944$

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$3|648$

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$3|216$

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$3|72$

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$3|24$

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$8$

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$\Rightarrow 5832=3^6\times 2^3=(\sqrt{2}{)}^6\times 3^6=(3\sqrt{2}{)}^6$

$\Rightarrow lo{g}_{3\sqrt{2}}5832=6$.