How do you calculate $log_11 (1/sqrt 11)$ ?

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Answer 1 · 2016-09-08T14:56:34

$log_11 ( 1/sqrt11)=-1/2$

The question being asked in this log form is..

$log_11 ( 1/sqrt11)$

"What index/power of 11 will give $1/sqrt11$ ?"

The answer is not immediately obvious, so let's use some of the laws of indices to change $1/sqrt11$ into a different form.

$1/sqrt11 = 1/11^(1/2) = 11^-(1/2)$

$log_11 11^(-1/2)$ is now obvious by inspection,
because we can see that 11 has the index $-1/2$

$log_11 ( 1/sqrt11)= -1/2$

We could also get to the same result by using the change of base law.

$log_11 ( 1/sqrt11) = (log (1/sqrt11))/log11 = -1/2$

How do you calculate log_11 (1/sqrt 11)log_11 (1/sqrt 11)?