Question 139914
{{{2log(3,Y)-log(3,(y+4))= 2}}}
{{{log(3,Y^2)-log(3,(y+4))= 2}}}
{{{log(3,(Y^2)/(y+4))= 2}}}

By basic definition of logarithms, 
{{{3^2 = (y^2)/(y+4) }}}

{{{9=(y^2)/(y+4) }}}


Multiply both sides of the equation by (y+4):
{{{9(y+4) = y^2}}}
{{{9y+36=y^2}}}
{{{y^2 - 9y -36=0}}}


It's a quadratic equation, but, lo and behold, IT FACTORS!!  Life is GOOD, isn't it??  (Well, sometimes!!)
 

{{{y^2 - 9y -36=0}}}
{{{(y-12)(y+3)=0}}}
{{{y=12}}} or {{{y=-3}}}


Reject the negative answer, since you can't have a log of a negative.

{{{y=12}}}


Please see my entire chapter on logarithms.  Go to my website by clicking on my tutor name "rapaljer" anywhere in algebra.com.  Take the second link, which is "Basic, Intermediate, or College Algebra: One Step at a Time."  Look for "College Algebra", "Chapter 4 Logarithms", "Section 4.04"!  This is an explanation on LOGARITHMS that was written for people who have a hard time understanding math!  I think if you have a hard time with logarithms, you will like this chapter!!!


R^2