# How do you simplify log_2 (4^2*3^4)?

Jan 12, 2017

$4 + 4 {\log}_{2} 3$

#### Explanation:

You would use some properties of logarithms:

1)$\log \left(a \cdot b\right) = \log a + \log b$

2)$\log {a}^{b} = b \log a$

then

${\log}_{2} \left({4}^{2} \cdot {3}^{4}\right) = {\log}_{2} \left({4}^{2}\right) + {\log}_{2} \left({3}^{4}\right)$$\to$property 1)

$= 2 {\log}_{2} 4 + 4 {\log}_{2} 3$ $\to$property 2)

Since ${\log}_{2} 4 = 2$,

the expression becomes

$2 \cdot 2 + 4 {\log}_{2} 3 = 4 + 4 {\log}_{2} 3$