Question 67199
Rules:
1. {{{highlight(ln(a)+ln(b)=ln(ab))}}}
2.  If {{{highlight(ln(a)=ln(b))}}} then {{{highlight(a=b)}}}
:
solve ln(x^2 + 12)=ln x + ln 8
{{{ln(x^2+12)=ln(8x)}}} rule 1
{{{x^2+12=8x}}} rule 2
{{{x^2-8x+12=8x-8x}}} set = to 0
{{{x^2-8x+12=0}}}
{{{(x-2)(x-6)=0}}} Factor
x-2=0  or  x-6=0
x-2+2=0+2  or x-6+6=0+6
x=2 or x=6
Check for extraneous solutions.
{{{ln((2)^2+12)=ln(2)+ln(8)}}}
{{{ln(4+12)=ln(2)+ln(8)}}}
{{{ln(16)=ln(2)+ln(8)}}}
2.772588722=.6931471806+2.079441542
2.772588722=2.772588722  x=2 is valid
{{{ln((6)^2+12)=ln(6)+ln(8)}}}
{{{ln(36+12)=1.791759469+2.079441542}}}
ln(48)=3.871201011
3.87201011=3.8712011  x=6 is valid, too.
{{{highlight(x=2)}}} or {{{highlight(x=6)}}}
Happy Calculating!!!