You can put this solution on YOUR website! Domain: The arguments to any logarithm function, no matter what the base, must always be positive. So to find the domain we just have to solve:
Adding x to both sides gives us which says x is less than 5. (Always read inequalities from where the variable is! In this case we read it from right to left, since x is on the right, which is why it is a less than.)
The domain is all numbers less than 5.
Vertical asymptote: For logarithm functions the vertical asymptote will be for x values that would make the argument zero. So we solve
Again adding x to both sides we get
So the vertical asymptote is the line: x = 5
The x-intercepts of a function is where the y-value is 0. So we need to solve
0 = log(base4)(5-x)
If we understand exponents and logarithms, this is easy. This equation says that 0 (zero) is the exponent you put on 4 to get (5-x). But a zero exponent on any number (except 0) always results on 1! So this equation means that (5-x) must be 1.
Solving
Subtract 5 from both sides giving
Dividing (or multiplying) both sides by -1 we get
So our only x-intercept is (4, 0).
(