Determine the average value of $f(x)$ over the interval from $x=a$ to $x=b$, where $f(x)=\frac{1}{x}, a=\frac{1}{6}$, and $b=6$. The average value is (Type an exact answer.)

Step 1 ：The average value of a function $f(x)$ over the interval $[a, b]$ is given by the formula: \(\frac{1}{b-a}\int_{a}^{b}f(x)dx\)

Step 2 ：In this case, $f(x) = \frac{1}{x}$, $a = \frac{1}{6}$, and $b = 6$. So we need to compute the integral of $f(x)$ from $a$ to $b$ and then divide by the length of the interval.

Step 3 ：The integral of $f(x)$ from $a$ to $b$ is $\ln|b| - \ln|a|$

Step 4 ：The length of the interval from $a$ to $b$ is $b - a$

Step 5 ：Substitute the values of $a$, $b$, and the integral of $f(x)$ from $a$ to $b$ into the formula for the average value of a function over an interval

Step 6 ：The average value of $f(x)$ over the interval from $x=a$ to $x=b$ is \(\boxed{0.307158766153381 + 0.171428571428571\log(6)}\)