How do you condense $ln2 + ln6 - (1/2)ln9$ ?

Question

7361 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-30T17:12:33

$ln2+ln6-(1/2)ln9=ln4$

We can use $lnx+lny=lnxy$ , $lnx-lny=ln(x/y)$ and $1/nlnx=ln(root(n)x)$

Hence, $ln2+ln6-(1/2)ln9$

= $ln(2xx6)-ln(sqrt9)$

= $ln12-ln3$

= $ln(12/3)=ln4$

How do you condense ln2 + ln6 - (1/2)ln9ln2 + ln6 - (1/2)ln9?