# How do you condense 1/2log8v+log8n-2log4n-1/2log2j?

Jun 19, 2016

$\log \left(\frac{1}{n} \sqrt{\frac{v}{j}}\right)$

#### Explanation:

By using log properties, you can write

$\log {\left(8 v\right)}^{\frac{1}{2}} + \log \left(8 n\right) - \log {\left(4 n\right)}^{2} - \log {\left(2 j\right)}^{\frac{1}{2}}$

and then, by grouping terms,

$\log \left(\frac{\sqrt{\textcolor{red}{8} v}}{\sqrt{\textcolor{red}{2} j}}\right) + \log \left(\frac{\textcolor{red}{8} \cancel{n}}{\textcolor{red}{16} {n}^{\cancel{2}}}\right)$

$= \log \left(\sqrt{\frac{\textcolor{red}{4} v}{j}}\right) + \log \left(\frac{1}{2 n}\right)$

By using again log properties, you obtain

$\log \left(\frac{1}{\cancel{2} n} \cancel{2} \sqrt{\frac{v}{j}}\right)$

$\log \left(\frac{1}{n} \sqrt{\frac{v}{j}}\right)$