3. Given that $a, b, c, d$ are positive integers, and
$$
\log _{a} b=\frac{3}{2}, \log _{c} d=\frac{5}{4}, a-c=9 \text {. }
$$

Then $a+b+c+d=$ $\qquad$ .
3. 198 .

Given the problem, let $a=x^{2}, b=x^{3}, c=y^{4}, d=y^{5}$.
From $a-c=x^{2}-y^{4}=9$
$\Rightarrow\left(x+y^{2}\right)\left(x-y^{2}\right)=9$
$\Rightarrow x+y^{2}=9, x-y^{2}=1$
$\Rightarrow x=5, y^{2}=4$
$$
\begin{array}{l}
\Rightarrow a=25, b=125, c=16, d=32 \\
\Rightarrow a+b+c+d=198 .
\end{array}
$$