What is the vertical asymptote of the graph of y=log4(x-3) ?

X=-3

To find the vertical asymptote of the graph of y = log4(x-3), we need to analyze the behavior of the function as x approaches certain values.

The vertical asymptote occurs when the function approaches positive or negative infinity as x gets closer to a specific value.

In this case, the function y = log4(x-3) has a vertical asymptote when the argument of the logarithm approaches zero.

Setting x - 3 equal to zero and solving for x gives us:

x - 3 = 0
x = 3

Therefore, the vertical asymptote of the graph of y = log4(x-3) is x = 3.

To determine the vertical asymptote of the graph of the function y=log4(x-3), we can analyze the properties of logarithmic functions.

Step 1: Recall that the logarithmic function log4(x) is undefined for x ≤ 0, as the logarithm of a non-positive number does not exist.
Therefore, the argument (x-3) in the given function must satisfy x-3 > 0 for the function to be defined.

Step 2: Set the argument (x-3) greater than zero and then solve for x:
x - 3 > 0
x > 3

Step 3: The value x = 3 serves as a vertical asymptote for the function y=log4(x-3). As x approaches 3 from the positive side, the function approaches negative infinity, indicating a vertical asymptote.

Thus, the vertical asymptote of the graph of y=log4(x-3) is the equation x = 3.

The domain of the log(x) function is for all non-negative values of x.

So what happens to log(x-3) when x-3 becomes zero?