How do you use the properties of logarithms to expand lnxyz^2lnxyz2?

1 Answer
Jan 7, 2017

lnx+lny+2lnzlnx+lny+2lnz

Explanation:

Since

log(ab)=loga+logblog(ab)=loga+logb,

then

ln(xyz^2)=lnx+lny+lnz^2ln(xyz2)=lnx+lny+lnz2

and, since

loga^b=blogalogab=bloga

then the given expression is:

lnx+lny+2lnzlnx+lny+2lnz