Final answer:
The equation of the tangent line to the graph of y = log4(x) at the point (64, 3) is found by taking the derivative to get the slope and then using the point-slope formula.
Step-by-step explanation:
To find the equation of the tangent line to the graph of the function y = log4(x) at the point (64, 3), we first need to calculate the derivative of the function, which will give us the slope of the tangent line at any point x. The derivative of y = log4(x) using the change of base formula and the derivative of the natural logarithm is y' = 1 / (x ln(4)). At the point x = 64, the slope will be m = 1 / (64 ln(4)). Since the point (64, 3) lies on the tangent, we can use the point-slope form y - y1 = m(x - x1) to find the equation of the tangent line.
Substituting the point (64, 3) and the slope m into the point-slope formula, we get y - 3 = (1 / (64 ln(4)))(x - 64). This is the equation of the tangent line at the point (64, 3) to the graph of y = log4(x).