Question 136379
{{{lnx +ln(x + 3) = 1}}}
{{{ln(x*(x + 3)) = 1}}}
Let {{{y = x*(x+3)}}}
Rewrite equation as
{{{ln(y) = 1}}}
Rewite this as
{{{e^1 = y}}}
or
{{{e = x*(x + 3)}}}
{{{x^2 + 3x = e}}}
Complete the square
{{{x^2 + 3x + (3/2)^2 = e + (3/2)^2}}}
{{{(x + (3/2))^2 = e + 9/4}}}
take square root of both sides
{{{x + (3/2) = 0 +-sqrt(e + 9/4)}}}
{{{x = -(3/2) +-sqrt(e + 9/4)}}} answer
(unless I goofed)