On which interval is log(5 – x) negative?
numbers between one and zero have negative logs ... 5 > x > 4
To determine on which interval the function log(5 - x) is negative, we need to find the values of x for which log(5 - x) is less than zero.
The logarithm function log(a) is negative if and only if a is between 0 and 1 exclusively.
Thus, we can write the inequality: 0 < 5 - x < 1
To solve this, we need to isolate x:
0 < 5 - x < 1
Subtract 5 from all sides:
-5 < -x < -4
Multiplying by -1 and reversing the inequality signs, we get:
4 < x < 5
So the function log(5 - x) is negative on the interval (4, 5).