How to solve this exponential inequality

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I'm really struggling with this inequality. It seems I should solve it using logarithms but have no idea how to it specifically. Can you help me with that? $(2^x)*(3^{1/x})>6$

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HINT

Take log both side and observe that log is strictly increasing, then

$$\iff x\log 2 + \frac1x \log 3 > \log 6$$

Can you proceed from here?