Question

\log_{2}(x-3) + \log_{2}(x) - \log_{2}(x+2) = 2

Answer 1

\[\log_{2}(x-3) + \log_{2}(x) - \log_{2}(x+2) = 2 \]

Answer 2

\[\log_2((x-3)x)-\log_3(x+2)=2\]
\[\log_2(\frac{x(x-2)}{x+2})=2\]
\[\frac{x(x-2)}{x+2}=2^2=4\]
\[x(x-2)=4(x+2)\] and now solve the quadratic

Answer 3

\[x^2-6x-8=0\]
\[x=3\pm\sqrt{17}\]
\[x=3+\sqrt{17}\] because the other one is negative