# How do you solve logx-log3 = log(x+8)?

Jan 27, 2016

$x = - 12$

#### Explanation:

Subtracting logs is the result from taking loges of a division

So $\log \left(x\right) - \log \left(3\right) \to \log \left(\frac{x}{3}\right)$

Write as $\textcolor{w h i t e}{. .} \log \left(\frac{x}{3}\right) = \log \left(x + 8\right)$

If this is true then it is also true that:

$\frac{x}{3} = x + 8$

$x = 3 x + 24 \to$ Multiplied both sides by 3

$2 x = - 24 \to$Collecting like terms and simplifying

$x = - 12 \to$ Divide both sides by 2