How do you use the properties of logarithms to rewrite(expand) each logarithmic expression log(3x^3 y^2)?

Jul 6, 2015

$\log \left(3 {x}^{3} {y}^{2}\right) = 3 \log x + 2 \log y + \log 3$

Explanation:

First Property: $\log \left(x y\right) = \log x + \log y$

So

$\log \left(3 {x}^{3} {y}^{2}\right) = \log 3 + \log \left({x}^{3}\right) + \log \left({y}^{2}\right)$

Second Property: $\log \left({x}^{d}\right) = \mathrm{dl} o g x$

So

$\log \left(3 {x}^{3} {y}^{2}\right) = \log 3 + \log \left({x}^{3}\right) + \log \left({y}^{2}\right) = \log 3 + 3 \log x + 2 \log y$

$\log \left(3 {x}^{3} {y}^{2}\right) = 3 \log x + 2 \log y + \log 3$