Homework help! I need steps please and answer?

Question

if 2log(x-2y)=log x+log y, evaluate x/y

2) Let f(x)=2x-1 and g(x) = ½ x +3 determine
(f-1 ◦ g) (x)
(g-1 ◦ f-1) (x)

f is raised to the power -1 not minus one

Thank you soooo much

Answer 1

1. log (x-2y)^2 = log (xy)

x^2 - 4xy + 4y^2 = xy

x^2 - 5xy + 4y^2 = 0

-5xy + 4y^2 = x^2

-5x + (4y)/x = x/y

2. I'll help you find the inverses. The rest should be easy.

f-1(x) = (x+1) / 2

g-1(x) = 2x - 6

Answer 2

2 log x - 2 log 2y = log x + log y
log x = 3 log (2y ) = log (2y )^3
x = ( 2y )^3 = 8 y^3
x/y = 8 y^2

Answer 3

2log(x-2y)=log x+log y
log (x-2y)^2 = log(xy)
(x-2y)^2 = xy
x^2-4xy +4y^2 =xy
x^2-5xy +4y^2= 0
x = [5y +/- sqrt(25y^2 - 16y^2)]/2 = [5y +/- 3y]/2 = y or 4y
So x/y = 1 or 4