# Log

Algebra Level 4

$2\log_x a + \log_{ax} a + 3\log_b a = 0$

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

If the solutions can be expressed as $$a^c$$ and $$a^d$$, and $$c + d$$ can be expressed as $$-\dfrac ef$$ for coprime positive integers $$e$$ and $$f$$, evaluate $$e-f$$.

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