Question 54934
The rules we're going to use are:
1.{{{highlight(ln(a)-ln(b)=ln(a/b))}}}
2. {{{highlight(ln(a)=b)}}}=>{{{highlight(a=e^b)}}}
3. {{{highlight(a^0=1)}}}
solve the equation ln(x+5)- ln(3)= ln (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}}} Rule 1
{{{(x+5)/(3(x-3))=e^0}}}  Rule 2
{{{(x+5)/(3(x-3))=1}}}  Rule 3
{{{3(x-3)(x+5)/(3(x-3))=3(x-3)(1)}}}
{{{cross(3(x-3))(x+5)/cross(3(x-3))=3(x-3)}}}
{{{x+5=3x-9}}}
{{{-x+x+5=-x+3x-9}}}
{{{5=2x-9}}}
{{{9+5=2x-9+9}}}
{{{14=2x}}}
{{{14/2=2x/2}}}
{{{7=x}}}
:
Check by subtituting 7 in for x's in the original equation and see if both sides equal once you simplify:
{{{ln(7+5)-ln(3)=ln(7-3)}}}
{{{ln(12)-ln(3)=ln(4)}}}
{{{ln(12/3)=ln(4)}}}  Rule 1
{{{ln(4)=ln(4)}}}  We're right!!!
Happy Calculating!!!