SOLUTION: help me solve ln(x^2 + 12)=ln x + ln 8

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Question 67199This question is from textbook
: help me solve ln(x^2 + 12)=ln x + ln 8 This question is from textbook

Found 2 solutions by bam878s, funmath:
Answer by bam878s(77) About Me  (Show Source):
You can put this solution on YOUR website!
This problem is simple once you utilize a common law of logarithms.
ln ab = ln a + ln b
On the right hand side of this equation we have ln x + ln 8. By using the above law, we can write this as ln 8x.
So, we have:
ln(x%5E2 + 12) = ln 8x. So now we know that x%5E2 + 12 = 8x
x%5E2 + 12 = 8x
x%5E2 + 12 - 8x = 0
x%5E2 - 8x + 12 = 0. We can solve this by using the quadratic formula, but an easier way would be to factor this out as follows:
x%5E2 - 8x + 12 = (x-6) * (x-2). So, we have:
(x-6)(x-2) = 0. We know that 0 * anything = 0, so now we can easily see that
x = 6 or x = 2.
Hope this helps!!

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Rules:
1. highlight%28ln%28a%29%2Bln%28b%29=ln%28ab%29%29
2. If highlight%28ln%28a%29=ln%28b%29%29 then highlight%28a=b%29
:
solve ln(x^2 + 12)=ln x + ln 8
ln%28x%5E2%2B12%29=ln%288x%29 rule 1
x%5E2%2B12=8x rule 2
x%5E2-8x%2B12=8x-8x set = to 0
x%5E2-8x%2B12=0
%28x-2%29%28x-6%29=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%28%282%29%5E2%2B12%29=ln%282%29%2Bln%288%29
ln%284%2B12%29=ln%282%29%2Bln%288%29
ln%2816%29=ln%282%29%2Bln%288%29
2.772588722=.6931471806+2.079441542
2.772588722=2.772588722 x=2 is valid
ln%28%286%29%5E2%2B12%29=ln%286%29%2Bln%288%29
ln%2836%2B12%29=1.791759469%2B2.079441542
ln(48)=3.871201011
3.87201011=3.8712011 x=6 is valid, too.
highlight%28x=2%29 or highlight%28x=6%29
Happy Calculating!!!