Let \( a, b, c, d \) are positive integers such that \( \log _{a} b...

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Let \( a, b, c, d \) are positive integers such that \( \log _{a} b=\frac{3}{2} \) and \( \log _{c} d=\frac{5}{4} \). If \( (a-c)=9 \), find the value of \( \frac{b+d}{a+c} \).
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