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

1 Answer
Dec 18, 2015

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