Question

How do you use the properties of lorgarithms to solve for x: In x + In(x-1)=In 2

Answer 1

ln x+ln (x-1)=ln2
ln (x)(x-1)=ln2
x^2-x=2
x^2-x-2=0
x^2-2x+x-2=0
x(x-2)+1(x-2)=0
(x-2)(x+!)=0
Either x-2=0,x=2
Or x+1=0,x=-1(Rejected ,because x>or=0,for log x to be defined)