ANSWER
x=100,y=10
EXPLANATION
The given logarithmic equations are;
[tex] log_{10}( {x}^{2} {y}^{3} ) = 7[/tex]
This implies that,
[tex] {x}^{2} {y}^{3} = {10}^{7} ...(1)[/tex]
and
[tex] log_{10}( \frac{x}{y} ) = 1[/tex]
This implies that,
[tex] \frac{x}{y} = {10}^{1} [/tex]
[tex]x = 10y...(2)[/tex]
Put equation (2) into equation (1)
[tex]{(10y)}^{2} {y}^{3} = {10}^{7}[/tex]
[tex]10 ^{2} y^{2} {y}^{3} = {10}^{7}[/tex]
[tex]{y}^{5} = {10}^{5}[/tex]
Hence y=10.
This implies
[tex]x = 10(10) = 100[/tex]
