# How do you write the logarithmic expression as the sum, difference, or multiple of logarithms and simplify as much as possible for log(9x^3)?

Jul 5, 2015

$\log \left(9 {x}^{3}\right) = 2 \log 3 + 3 \log x$

#### Explanation:

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

So

$\log \left(9 {x}^{3}\right) = \log 9 + \log \left({x}^{3}\right) = \log \left({3}^{2}\right) + \log \left({x}^{3}\right)$

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

So

$\log \left(9 {x}^{3}\right) = 2 \log 3 + 3 \log x$