If log10(x^2y^3) =7 and log 10(x/y) =1 then x = blank and y= blank

log10(x^2y^3) =7                             log 10(x/y) =1

log (x^2) + log (y^3) = 7                  log x - log y = 1

2 log (x) + 3 log y =7                        log x = 1 + log y

substitute in

2 (1 + log y) + 3 log y =7

2 + 2 log y + 3 log y =7

2 +5 log y =7

subtract 2 from each side

5 log y =5

log y  =1

take the inverse of each side

y = 10^1

y =10

 log x = 1 + log y

log x = 1 + 1

log x =2

x = 10^2

x = 100