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Algebra Level 5

2logxa+logaxa+3logba=0 2\log_x a + \log_{ax} a + 3\log_b a = 0

For a>0a>0 and b=a2xb=a^2 x, solve the equation above.

If the solutions can be expressed as aca^c and ada^d, and c+dc + d can be expressed as ef-\dfrac ef for coprime positive integers ee and ff, evaluate efe-f.

This is part of the set My Problems and THRILLER

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