Find the average value of the function $f(x)=\frac{6}{x}$ on the interval $[1,4]$. \[ f_{\text {ave }}= \]

Step 1 ：Define the function \(f(x)=\frac{6}{x}\).

Step 2 ：Calculate the integral of the function \(f(x)=\frac{6}{x}\) from 1 to 4, which is \(6\log(4)\).

Step 3 ：Divide the integral by the length of the interval to find the average value, which is \(2\log(4)\).

Step 4 ：\(\boxed{2\log(4)}\) is the average value of the function \(f(x)=\frac{6}{x}\) on the interval \([1,4]\).