Exponential & Log Functions

Question

 

State the restriction(s) on the variable x in log(2x-5) – log (4 - x) 

Answer 1

Logarithmic functions cannot take an argument that is less than or equal to 0 (convince yourself of this). Thus, any argument must be greater than 0. The two arguments that you are looking at are 2x - 5 and 4 - x. We set up our inequalities and solve for x:

2x - 5 > 0

2x > 5

x > 5/2

4 - x > 0

4 > x

Thus, we have obtained bounds on x such that 5/2 < x < 4. We can also say that x must be in the interval (5/2, 4), or x ∈ (5/2, 4).