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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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