How do you condense log_2 4+ 3log_2 9?

Oct 12, 2016

${\log}_{2} \left(4\right) + 3 {\log}_{2} \left(9\right) = {\log}_{2} \left(2916\right) \approx 11.5$

Explanation:

We will use the following properties of logarithms:

• $x {\log}_{a} \left(b\right) = {\log}_{a} \left({b}^{x}\right)$
• ${\log}_{a} \left(x\right) + {\log}_{a} \left(y\right) = {\log}_{a} \left(x y\right)$

With those, we have

${\log}_{2} \left(4\right) + 3 {\log}_{2} \left(9\right) = {\log}_{2} \left(4\right) + {\log}_{2} \left({9}^{3}\right)$

$= {\log}_{2} \left(4 \cdot {9}^{3}\right)$

$= {\log}_{2} \left(2916\right)$