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log2x+log8x+log64x=logx2+logx16+logx128 \large \log_{2}x +\log_{8}x+\log_{64}x = \log_{x}2+\log_{x}16+\log_{x}128 log2x+log8x+log64x=logx2+logx16+logx128
Let xxx be a real number satisfying the equation above.
If the value of log2x+logx2\log_{2}x + \log_{x}2log2x+logx2 can be expressed as abc\dfrac{a\sqrt{b}}{c}cab , where aaa and ccc are coprime positive integers and bbb is square-free, compute abc.abc.abc.
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