Algebra question
Medium · from the problemset algebra collection
03
$$\text{If } 2\log_x7+\log_{7x}7_+3\log_{49x}7=0 \text{ has two solutions } \alpha \text{ and } \beta \text{ then find } \alpha^{\frac{-3}{4}}+\beta^{-2} \\ \text{ such that both }
\alpha^{\frac{-3}{4}},\beta^{-2}\in \mathbb{Z}^{+}.$$
