How do you use the properties of logarithms to expand $ln x y z^{2}$ $lnxyz^2$ ?

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Answer 1 · 2017-01-07T06:27:55

$ln x + ln y + 2 ln z$ $lnx+lny+2lnz$

Since

$log (a b) = log a + log b$ $log(ab)=loga+logb$ ,

then

$ln (x y z^{2}) = ln x + ln y + {ln z}^{2}$ $ln(xyz^2)=lnx+lny+lnz^2$

and, since

${log a}^{b} = b log a$ $loga^b=bloga$

then the given expression is:

$ln x + ln y + 2 ln z$ $lnx+lny+2lnz$

How do you use the properties of logarithms to expand lnxyz2lnxyz^2?