# How do you solve the equation log_4a+log_4 9=log_4 27?

Oct 27, 2016

$a = 3$

#### Explanation:

${\log}_{4} a + {\log}_{4} 9 = {\log}_{4} 27$

${\log}_{4} a + {\log}_{4} 9 - {\log}_{4} 27 = 0$

${\log}_{4} \left(\frac{9 a}{27}\right) = 0$----->Use properties ${\log}_{b} x + {\log}_{b} y = {\log}_{b} \left(x y\right)$ and ${\log}_{b} x - {\log}_{b} y = {\log}_{b} \left(\frac{x}{y}\right)$

${4}^{0} = \frac{9 a}{27}$

$1 = \frac{9 a}{27}$

$27 = 9 a$

$a = 3$