Question

How do you solve `log(5+x)-log(x-3)=log3`?

Answer 1

`color(white)(xx)x=7`

Explanation:

`color(white)(xx)log(5+x)-log(x-3)=log3`

The quotient of two positive numbers are calculated as difference of their logarithms. Therefore,
`=>log((5+x)/(x-3))=log3`
`=>(5+x)/(x-3)=3`
`=>3x-9=5+x`

`=>3x-9color(red)(-x+9)=5+xcolor(red)(-x+9)`
`=>color(red)(1/2xx)2x=color(red)(1/2xx)14`

`=>x=7`