Let `a , b , c , d` be positive integers such that `(log)_a b=3/2a n d(log)_c d=5/4dot` If `(a-c)=9,` then find the value of `(b-d)dot`

Explanation

To solve the problem step by step, we start with the given equations and conditions:

1. We know that:
\[ \log_a b = \frac{3}{2} \quad \text{and} \quad \log_c d = \frac{5}{4} \]
From the properties of logarithms, we can rewrite these equations in exponential form:
\[
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