log(n) is defined only for n > 0.
So, we must have x-2 > 0 or x>2
and 3x-5 > 0 or x > 5/3
Combining those conditions, we see we must have x>2. That will make both expressions positive.
What are the restrictions on the variable x in the following equation? Why do these restrictions exist?
log(x-2)-log(3x-5)=5
Thanks for your help :-)
2 answers
Since we cannot take Log of zero, x-2
cannot equal 0. In other words, x cannot equal 2. So x can be any real
number except 2:
X < > 2.
Also, 3x - 5 cannot equal 0:
3x-5 = 0,
3x = 5,
X = 5/3.
So x should be less than or greater than 5/3:
X < > 5/3.
cannot equal 0. In other words, x cannot equal 2. So x can be any real
number except 2:
X < > 2.
Also, 3x - 5 cannot equal 0:
3x-5 = 0,
3x = 5,
X = 5/3.
So x should be less than or greater than 5/3:
X < > 5/3.