How do you evaluate the expression log_11(11^(n-5))?

Oct 17, 2016

The expression can be simplified to $n - 5$.

Explanation:

Start by simplifying the expression using the rule $\log {n}^{a} = a \log n$.

$= \left(n - 5\right) {\log}_{11} \left(11\right)$

Now, simplify using the formula ${\log}_{a} \left(n\right) = \log \frac{n}{\log} a$.

$= \left(n - 5\right) \log \frac{11}{\log} 11$

$= \left(n - 5\right) \left(1\right)$

$= n - 5$

Hopefully this helps!