How do you evaluate the expression ${log}_{11} (11^{n - 5})$ $log_11(11^(n-5))$ ?

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Answer 1 · 2016-10-17T14:55:00

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

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

$= (n - 5) {log}_{11} (11)$ $=(n - 5)log_11(11)$

Now, simplify using the formula ${log}_{a} (n) = \frac{log n}{log a}$ $log_a(n) = logn/loga$ .

$= (n - 5) \frac{log 11}{log 11}$ $=(n - 5)log11/log11$

$= (n - 5) (1)$ $=(n - 5)(1)$

$= n - 5$ $= n - 5$

Hopefully this helps!

How do you evaluate the expression log11(11n−5)log_11(11^(n-5))?