How do you solve $log_11(sqrt(11^7))=n$ ?

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Answer 1 · 2015-11-30T22:50:58

$n=7/2$

The first step to take is rewriting $sqrt(11^7)$ as $(11^7)^(1/2)$ , which equals $11^(7/2)$ .

So, we now have:

$log_11 11^(7/2)=n$

Now, we can use the following rule: $log_a b^c=clog_a b$ .

We get:

$7/2log_11 11=n$

Since $log_a a=1$ , we know that $log_11 11=1$ .

Therefore, $n=7/2$ .

How do you solve log_11(sqrt(11^7))=nlog_11(sqrt(11^7))=n?