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

Nov 30, 2015

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

#### Explanation:

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

So, we now have:

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

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

We get:

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

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

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