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 $f^{\prime }(x)=\frac{4(\ln x{)}^3}{x}$.

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 ：$\boxed{{\displaystyle y=0.67x-1.10}}$ is the final answer.