Final answer:
The slope of the line tangent to the graph of y = ln(2x) at the point where x = 4 is 0.5, which is found by taking the derivative of the function and evaluating it at x = 4.
Step-by-step explanation:
The slope of the line tangent to the graph at a certain point is the derivative of the function at that point.
To find the slope of the line tangent to the graph of y = ln(2x) at the point where x = 4, we first need to take the derivative of the function.
The derivative of ln(2x) with respect to x is 1/x multiplied by the derivative of 2x, which is 2.
So, the derivative of y with respect to x is 2/x. Plugging in the value x = 4, we get 2/4 = 0.5. Therefore, the slope of the tangent line at x = 4 is 0.5.