Solve the equation. log⁡(x+2)−log⁡x=2log⁡4

Step 1 Given equation
$\log (x+2)-\log x=2\log 4$
Step 2 Formula
${\displaystyle \log a-\log b=\frac{\log a}{\log b}}$
${\displaystyle \log \left(ab\right)=\log a\times \log b}$
${\displaystyle {\log x}^n=n\log x}$
Step 3 We need to solve the equation
${\displaystyle \log (x+2)-\log x=2\log 4}$
${\displaystyle \frac{\log (x+2)}{\log x}=2\log 4}$
${\displaystyle \frac{\log (x+2)}{\log x}={\log 4}^2}$
Taking anti−log on both sides
${\displaystyle \frac{x+2}{x}=16}$
x+2=16x
16-x=2
15x=2
${\displaystyle x=\frac{2}{15}}$
Step 4 Answer
${\displaystyle x=\frac{2}{15}}$