Question

log(x-5)=log4-log(x+2)

Answer 1

How do you condense the right side so that you can eliminate the log?

Answer 2

let me give you a hint:
\[\log(a)-\log(b)=\log \left( \frac{a}{b} \right)\]

Answer 3

\[\huge\color{blue}{ \log(x-5)=\log(4)-\log(x+2) } \]\[\huge\color{blue}{ \log(x-5)=\log(\color{red} { 4 })-\log(\color{red} { x+2 }) } \]\[\huge\color{blue}{ \log(x-5)=\log(\color{blue} { \frac{\color{red} { 4 }}{\color{red} { x+2 }} }) } \]
\[\huge\color{blue}{ x-5=\frac{4}{x+2} } \]
\[\huge\color{blue}{ \frac{x-5}{1}=\frac{4}{x+2} } \]
\[\huge\color{blue}{ (x-5)(x+2)=1 \times 4 } \]
\[\huge\color{blue}{x^2-3x-10=4 } \]

can you solve this quadratic?