# How do you use the properties of logarithms to expand log_10 (4x^2y)?

Aug 6, 2017

See below.

#### Explanation:

Remember that $\setminus {\log}_{10} \left(a b\right) = {\log}_{10} a + {\log}_{10} b$

So,

${\log}_{10} \left(4 {x}^{2} y\right) = {\log}_{10} \left(4\right) + {\log}_{10} \left({x}^{2}\right) + {\log}_{10} \left(y\right)$

In addition, $\setminus {\log}_{10} \left({a}^{2}\right) = 2 {\log}_{10} a$

So,

${\log}_{10} \left(4\right) + {\log}_{10} \left({x}^{2}\right) + {\log}_{10} \left(y\right) = 2 {\log}_{10} \left(2\right) + 2 {\log}_{10} \left(x\right) + {\log}_{10} \left(y\right)$