Question 64825
SOLVE THE EQUATION In(x+5)-In(3)=In(x-3).
{{{ln(x+5)-ln(3)-ln(x-3)=ln(x-3)-ln(x-3)}}}
{{{ln(x+5)-ln(3)-ln(x-3)=0}}}
{{{ln((x+5)/(3(x-3)))=0}}}
{{{(x+5)/(3(x-3))=e^0}}}
{{{(x+5)/(3x-9)=1}}}
{{{(3x-9)(x+5)/(3x-9)=(3x-9)(1)}}}
{{{cross((3x-9))(x+5)/(cross((3x-9)))=3x-9}}}
{{{x+5=3x-9}}}
{{{x-x+5=3x-x-9}}}
{{{5=2x-9}}}
{{{5+9=2x-9+9}}}
{{{14=2x}}}
{{{14/2=2x/2}}}
{{{7=x}}}
Check for extraneous solutions:
{{{ln(7+5)-ln(3)=ln(7-3)}}}
{{{ln(12)-ln(3)=ln(4)}}}
{{{ln(12/3)=ln(4)}}}
{{{ln(4)=ln(4)}}}  The solution x=7 is valid.
Happy Calculating!!!