Question

Find the domain of f(x) = ln(5 − x).

Answer 1

x<5 and x<0

Answer 2

From the definition of ln
\[e^y=5-x\] (if you subbed any number into y for this equation you would never get zero or a negative)
From this definition you can see that
5-(x) > 0

Therefore you can deduce that any positive number greater than 5 that you place into this equation you will end up with a negative.
Although if you insert anything close to anything below or close to 5 you will end up with a positive.

for example -1
5-(-1) > 0
a negative multiplied by a negative is a positive thus you have 6
5+1 = 6 and 6>0

Thus your domain of definition is (negative infinity, 5)
please note that I used round brackets instead of square brackets because the number set does not include 5 as the equation cannot be equal to zero. With infinities always use round brackets.

Hope this is easy enough for you