Question 70987
{{{log X +log (X + 2) = log 3}}}
{{{log(x^2+2x)=log 3}}}Combine logs using basic identity log(x)+log(y)=log(x*y)
{{{cross(10)^(log(x^2+2x))=cross(10)^(log 3)}}}Cancel out logs by making the base 10 with the equation as a raised power (which undoes the logs with base 10)
{{{x^2+2x=3}}}Now you have an equation in which you can solve for x
{{{(x-1)(x+3)=0}}}Get everything to one side and factor it, then solve for x
{{{x=1}}} and {{{x=-3}}} are your solutions. But wait, we're not done yet. We need to check these answers
Check:
Let x=1
{{{log (1)+ log (3)=log 3}}}
{{{log (1*3) = log 3}}}
{{{log 3= log 3}}} Answer works
Let x=-3
{{{log ((-3)) + log ((-3+2))=log 3}}} You cannot take the log of a negative number  (if you want a real number) so this solution does not work.
So the the only solution that works is x=1