How do i solve

Question

ln(x+1)=ln(x+3)-lnx?

Answer 1

The logarithmic equation ln(x + 1)= ln(x + 3) - ln(x)

{Apply quotient rule in logarithms ln(a) - ln(b) = ln(a/b)}

ln(x + 1) = ln[(x + 3)/x]

{Recall ln(a) =  ln(b) then a must equal to b}

x + 1 = (x + 3)/x

x(x + 1) = x + 3

x² + x = x + 3

x² = 3

Apply square root on each side.

Solution x = 1.7321.