# How do you solve 2 Log (x+7) = Log 9?

Dec 3, 2015

$x = - 4$

#### Explanation:

$2 \cdot \log \left(x + 7\right) = \log 9$
$\implies \frac{1}{2} \cdot 2 \cdot \log \left(x + 7\right) = \frac{1}{2} \cdot \log 9$
$\implies \log \left(x + 7\right) = \log \left({9}^{\frac{1}{2}}\right)$ (the logarithm of a second root is the logarithm of the number divided by 2)
$\implies \log \left(x + 7\right) = \log 3$
$\implies x + 7 = {10}^{\log} 3$
$x + 7 - 7 = 3 - 7$
$\implies x = - 4$