Yet another log

Algebra Level 4

Given log⁡ab=32\log_{a} b = \dfrac{3}{2} and log⁡cd=54\log_{c} d=\dfrac{5}{4}.

If a−c=9a-c=9 , then find the unique integral value of b−db-d.

Credit: 2003 Shaanxi Competition Problem 10

Prince Loomba by Prince Loomba
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