How do you find the domain of the function: f(x) = ln(x+4) + ln(8-5x)

Please help :(

What restricts the domain? The fact that the argument of ln has to be positive. So there are two restrictions x has to satisfy.

x + 4 > 0
8 - 5x > 0

Work out the set of x satisfying both of those. That's the domain.

domain consists of all real values of x for which f(x) is defined and real. Since logarithm functions are defined only for positive values of the argument, the domain of f(x) can only contain values of x for which x+4 and 8-5x are greater than zero.

x+4 > 0 ==> x > -4
8-5x > 0 ==> 8 > 5x ==> x < 8/5

The domain of the function are all the values of x that are greater than -4 and less than 8/5:
-4 < x < 8/5

The term inside of the natural logs must be greater than zero.
ln(x+4) --> x+4 > 0, x > -4, x is greater than -4
ln(8-5x) --> 8 - 5x > 0, x < 8/5 x is greater than 8/5
Therefore, the domain must be (-4, 8/5)

u mustn't have zero or Negative numbers in Parenthesis coz it doesn't mean.

so x+4>0 x>-4

and 8-5x>0 5x<8