CMIC Contest Question

Algebra Level 4

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

Let xx be a real number satisfying the equation above.

If the value of log2x+logx2\log_{2}x + \log_{x}2 can be expressed as abc\dfrac{a\sqrt{b}}{c} , where aa and cc are coprime positive integers and bb is square-free, compute abc.abc.

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