How do you solve ${log}_{11} (\sqrt{11^{7}}) = n$ $log_11(sqrt(11^7))=n$ ?

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How do you solve ${log}_{11} (\sqrt{11^{7}}) = n$ $log_11(sqrt(11^7))=n$ ?

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Answer 1 · 2015-11-30T22:50:58

$n = \frac{7}{2}$ $n=7/2$

Explanation:

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

So, we now have:

${log}_{11} 11^{\frac{7}{2}} = n$ $log_11 11^(7/2)=n$

Now, we can use the following rule: ${log}_{a} b^{c} = c {log}_{a} b$ $log_a b^c=clog_a b$ .

We get:

$\frac{7}{2} {log}_{11} 11 = n$ $7/2log_11 11=n$

Since ${log}_{a} a = 1$ $log_a a=1$ , we know that ${log}_{11} 11 = 1$ $log_11 11=1$ .

Therefore, $n = \frac{7}{2}$ $n=7/2$ .

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How do you solve ${log}_{11} (\sqrt{11^{7}}) = n$ $log_11(sqrt(11^7))=n$ ?

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Explanation:

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