Find the equation of the line tangent to the graph of $f(x)=(\ln x)^{4}$ at $x=2$. \[ y= \] (Type your answer in slope-intercept form. Do not round until the final answer. Then round to two decimal places as needed.)

Step 1 ：Let's find the derivative of the function \(f(x)=(\ln x)^{4}\).

Step 2 ：The derivative of the function is \(f'(x) = \frac{4(\ln x)^{3}}{x}\).

Step 3 ：Substitute \(x=2\) into the derivative to find the slope of the tangent line at that point.

Step 4 ：The slope of the tangent line at \(x=2\) is approximately 0.67.

Step 5 ：Substitute \(x=2\) into the original function to find the y-coordinate of the point of tangency.

Step 6 ：The y-coordinate of the point of tangency is \((\ln 2)^{4}\).

Step 7 ：Use the point-slope form of the line equation to find the equation of the tangent line.

Step 8 ：The equation of the line tangent to the graph of \(f(x)=(\ln x)^{4}\) at \(x=2\) is \(y=0.67x - 1.10\).

Step 9 ：\(\boxed{y=0.67x - 1.10}\) is the final answer.