Solve for x and y in the logarithmic system of equations:

Question

log{3}(x-2y)+ log{3}(3x+2y) = 3.

Answer 1

log{3}(x-2y)+ log{3}(3x+2y) = 3.

Using the product rule log_a x + log_a y =log_a (xy)

log{3}(x-2y)(3x+2y) = 3.

Using basic definition of the logathim

log_a x = N means that a^N = x.

(x-2y)(3x+2y) =3^3

(x-2y)(3x+2y) =27