Real variables x and y are related by the equation: ln(20y+16) - ln(4-y) = ln(2x+4) + ln(3-x)?

Question

need to give the range of values of x and y for which the expressions on each side of this equation are defined

Answer 1

ln(x) is defined for any x>0.

Hence:
1.
20y+16>0
20y>-16
y>-16/20=-4/5

2.
4-y>0
y<4

=> -4/5 < y < 4

3.
2x+4>0
2x>-4
x>-2

4.
3-x>0
x<3

=> -2 < x < 3

Answer 2

First let´s write the conditions of existence
20y+16>0 so y>-16/20 y> -4/5

4-y>0 so y<4 the condition for the first side are -4/5
2x+4>0 x>-2

3-x>0 x<3 range for the second side -2