if logxy3 and logxy1 find the values of x and y Could someon

if log(xy)=3 and log(x/y)=1, find the values of x and y

Could someone walk me through this.

Solution

log ( xy ) = 3

log (x/y ) = 1

applying log properties

log x + log y = 3

log x - log y = 1

adding the 2 equations

2 log x = 4

log x = 2

x = 10^2 = 100

log x + log y = 3

2 + log y = 3

log y = 1

y = 10

hence, x = 100 , y = 10