# How do you condense [1 - 5log_3x]/2 ?

Aug 29, 2015

${\log}_{3} {\left(\frac{3}{x} ^ 5\right)}^{\frac{1}{2}} \text{ or } {\log}_{3} \sqrt{\frac{3}{x} ^ 5}$

#### Explanation:

I assume that "condense" means "write as a single logarithm of a single expression". (I assume that because that's what I mean when I tell students to condense such an expression.)

$\frac{1 - 5 {\log}_{3} x}{2} = \frac{1}{2} \left(1 - 5 {\log}_{3} x\right)$

$= \frac{1}{2} \left(1 - {\log}_{3} {x}^{5}\right)$

$= \frac{1}{2} \left({\log}_{3} 3 - {\log}_{3} {x}^{5}\right)$

$= \frac{1}{2} {\log}_{3} \left(\frac{3}{x} ^ 5\right)$

$= {\log}_{3} {\left(\frac{3}{x} ^ 5\right)}^{\frac{1}{2}} \text{ or } {\log}_{3} \sqrt{\frac{3}{x} ^ 5}$