Solve the System of equations help! (has logs)

log(x) - log (y) =1
x+2y = 20

Thank you in advance :)

log(x) - log (y) =1
log(x/y) = 1
x/y = 10^1
x/y=10
x=10y

x+2y=20
10y+2y=20
12y=20
y=20/12

y=5/3

x=10y =10(5/3) = 50/3

I'm assuming by log you mean log base 10. The logic's the same for any other base, but the numbers are different.

By a property of logs, log(x) - log(y) = log(x / y).
Thus, log(x / y) = 1.
Then 10^log(x / y) = 10 ^ 1.
Thus, x / y = 10.
Therefore, x = 10y.
Substituting into the second equation, we get 10y + 2y = 20.
Then y = 20/12 = 5/3.
Thus, x = 50/3.

Hope this helps.

log(x) - log(y) = log(x/y) . . . by the properties of logarithms

10^1 = x/y . . . switching to exponential form

x/y = 10
x+2y = 20

Try it now.

what the person below said