# How do you write the logarithmic expressions as a single logarithm 2log_2)6 - 4)log_2y?

Oct 24, 2015

This expression can be written as ${\log}_{2} \left(\frac{36}{y} ^ 4\right)$

#### Explanation:

I assume that the brackets are here just by mistake because there are only closing brackets, so the correct expression is:

$2 {\log}_{2} 6 - 4 {\log}_{2} y$

This expression can be rewritten as follows:

$2 {\log}_{2} 6 - 4 {\log}_{2} y = {\log}_{2} {6}^{2} - {\log}_{2} {y}^{4} = {\log}_{2} \left(\frac{36}{y} ^ 4\right)$

The first step uses the property of logarythms which says that:

## $n \cdot {\log}_{a} b = {\log}_{a} {b}^{n}$ 

The last step uses the property which says that: