Huh "Solve"!!

Algebra Level 5

Solve $\log_{10} {x}+\log_{10} {1/2}+\log_{10} {1/4}+…=y$ And $\frac{1+3+5+7+…+(2y-1)}{4+7+10+…+(3y+1)}=\frac{20}{7\log_{10} {x}}$ Where $$x$$ and $$y$$ are positive integers which can be expressed as $x=\alpha^{\beta}$ and $y=\alpha$ What is $\alpha+\beta$ $$x, y \in R$$

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